user-1: ...if not, then who or what is governing these occurrences?
In the Diamond Sutta (see excerpt below) Buddha mentions the previous Buddha as being called Dīpankara Buddha possibly existing around ten thousand years ago. Then came Gautama Buddha and the next Buddha to occur could be Maitreya Buddha. Buddha also mentions here that there have been 84,000 multi-million Buddhas. I have no resistance about the existence of these Buddhas especially since losing the perception of chronological time, but when I observe sentient forms, there is - for the most part - some kind of growth or expansion of some sort happening with no real, tangible or perceivable force behind it.
With such a huge time span between the appearance of Buddhas it's perplexing to see this as either an evolutionary cosmological expansion of consciousness or... somebody somewhere sending in the forces in the same way that a declining school receives a new headmaster to try and rectify the mess.
Is anything regarding this mentioned in any of the major Buddhist schools of thought?

"Furthermore, Subhuti, if a son or daughter of good family, while reciting and practicing this sutra, is disdained or slandered, his or her misdeeds committed in past lives, including those that could bring about an evil destiny, will be eradicated, and he or she will attain the fruit of the most fulfilled, awakened mind. Subhuti, in ancient times before I met Buddha Dipankara, I had made offerings to and had been attendant of all 84,000 multi-millions of Buddhas. If someone is able to receive, recite, study, and practice this sutra in the last epoch, the happiness brought about by this virtuous act is hundreds of thousands times greater than that which I brought about in ancient times. In fact, such happiness cannot be conceived or compared with anything, even mathematically. Such happiness is immeasurable.

Apparently, there are 'ages' that have been defined...

Degeneration
Traditionally, this age [degeneration] is supposed to begin 2000 years
after Gautama Buddha's passing and last for "10,000 years". The first
two ages are the Age of Right Dharma
followed by the Age of Semblance Dharma. During this degenerate
third age, it is believed that people will be unable to attain
enlightenment through the word of Sakyamuni Buddha, and society will
become morally corrupt. In Buddhist thought, during the Age of Dharma
Decline the teachings of the Buddha will still be correct, but people
will no longer be capable of following them.


user362: Deepangkara Buddha was born before Kondangna Buddha but the aeons between the two births are uncountable. 

user-1: Today I found this which seems to answer this question.

Chiggala Sutta: The Hole
"Monks, suppose that this great earth were totally covered with water, and a man were to toss a yoke with a single hole there. A wind
from the east would push it west, a wind from the west would push it
east. A wind from the north would push it south, a wind from the south
would push it north. And suppose a blind sea-turtle were there. It
would come to the surface once every one hundred years. Now what do
you think: would that blind sea-turtle, coming to the surface once
every one hundred years, stick his neck into the yoke with a single
hole?"
"It would be a sheer coincidence, lord, that the blind sea-turtle,
coming to the surface once every one hundred years, would stick his
neck into the yoke with a single hole."
"It's likewise a sheer coincidence that one obtains the human state.
It's likewise a sheer coincidence that a Tathagata, worthy & rightly
self-awakened, arises in the world. It's likewise a sheer
coincidence that a doctrine & discipline expounded by a Tathagata
appears in the world. Now, this human state has been obtained. A
Tathagata, worthy & rightly self-awakened, has arisen in the world. A
doctrine & discipline expounded by a Tathagata appears in the world.
"Therefore your duty is the contemplation, 'This is stress... This is
the origination of stress... This is the cessation of stress.' Your
duty is the contemplation, 'This is the path of practice leading to
the cessation of stress.'"


user-1: ...cosmological evolutionary occurrence?
By 'evolutionary' if you mean a random event as like a 'random mutation in biological evolution', then NO. It's definitely a cosmological event as in, the attainment of Nirvana by a would be Buddha is a Cosmological Phenomena it's not a trivial case of altered consciousness of a Human.
...if not, then who or what is governing these occurrences?
There is No-Self and definitely no higher being controlling anything according to Buddhist Cosmology and Philosophy in general.
The Occurrence of a Buddha
It has vastly to do with two things;

The Karma of the would be Buddha, we are all potential would be Buddhas, our individual Karma will determine who would end up being one. With each act of Kindness and each Unwholesome deed, we birth our future.

The conditions for the arrival of the Buddha should be adequate, for e.g. The Buddha would not have born in say for an e.g. ancient Egypt because people were not into meditation nor would He have found bhikkus to memorise his suttas and pass on, He would not have born in British India or the Islamic India, He will not be born in Antartic or Arctic, etc you get my point. For a Buddha to carry out His operation of teaching the Dhamma to the fellow Humans, the conditions of His arrivals have to meet a certain environment, a milieu.


Finally, ponder upon this simile,

The Buddha used a sea turtle to illustrate the precious rarity of opportunity afforded by our human birth.  The turtle example appears in the scripture called in Pali, the Chiggala Sutta that is classified as LVI.48 of the Samyutta Nikaya.
"Monks, suppose that this great earth were totally covered with water,
and a man were to toss a yoke with a single hole there.
A wind from the east would push it west, a wind from the west would
push it east.  A wind from the north would push it south, a wind from
the south would push it north.
And suppose a blind turtle were there.  It would come to the surface
once every one hundred years.
Now what do you think - Would that blind turtle, coming to the surface
once every one hundred years, stick his neck into the yoke with a
single hole?"
"It would be a sheer coincidence, Lord, that the blind turtle, coming
to the   surface once every one hundred years, would stick his neck
into the yoke with a single hole."
"It's likewise a sheer coincidence that one obtains the human state.
It's likewise a sheer coincidence that a Tathagata, worthy and rightly
self-awakened, arises in the world.
It's likewise a sheer coincidence that doctrine and discipline
expounded by a Tathagata appears in the world.
Now, this human state has been obtained. A Tathagata, worthy and
rightly self-awakened, has arisen in the world. A doctrine and
discipline expounded by a Tathagata appears in the world.
"Therefore your duty is the contemplation: `This is stress . . .  .
This is the origination of stress . . .  . This is the cessation of
stress . . .  . This is the path of practice leading to the cessation
of stress."


-1: <p>...if not, then who or what is governing these occurrences?</p>
<p>In the Diamond Sutta (see excerpt below) Buddha mentions the previous Buddha as being called Dīpankara Buddha possibly existing around ten thousand years ago. Then came Gautama Buddha and the next Buddha to occur could be Maitreya Buddha. Buddha also mentions here that there have been 84,000 multi-million Buddhas. I have no resistance about the existence of these Buddhas especially since losing the perception of chronological time, but when I observe sentient forms, there is - for the most part - some kind of growth or expansion of some sort happening with no real, tangible or perceivable force behind it.</p>
<p>With such a huge time span between the appearance of Buddhas it's perplexing to see this as either an evolutionary cosmological expansion of consciousness or... somebody somewhere sending in the forces in the same way that a declining school receives a new headmaster to try and rectify the mess.</p>
<p>Is anything regarding this mentioned in any of the major Buddhist schools of thought?</p>
<blockquote>
<p>&quot;Furthermore, Subhuti, if a son or daughter of good family, while reciting and practicing this sutra, is disdained or slandered, his or her misdeeds committed in past lives, including those that could bring about an evil destiny, will be eradicated, and he or she will attain the fruit of the most fulfilled, awakened mind. Subhuti, in ancient times before I met <strong>Buddha Dipankara</strong>, I had made offerings to and had been attendant of all <strong>84,000 multi-millions of Buddhas</strong>. If someone is able to receive, recite, study, and practice this sutra in the last epoch, the happiness brought about by this virtuous act is hundreds of thousands times greater than that which I brought about in ancient times. In fact, such happiness cannot be conceived or compared with anything, even mathematically. Such happiness is immeasurable.</p>
</blockquote>
<p>Apparently, there are 'ages' that have been defined...</p>
<blockquote>
<p><a href="https://en.wikipedia.org/wiki/Three_Ages_of_Buddhism#Degeneration" rel="nofollow noreferrer">Degeneration</a></p>
<p>Traditionally, this age [degeneration] is supposed to begin 2000 years
after Gautama Buddha's passing and last for &quot;10,000 years&quot;. The first
two ages are the Age of Right Dharma
followed by the Age of Semblance Dharma. During this degenerate
third age, it is believed that people will be unable to attain
enlightenment through the word of Sakyamuni Buddha, and society will
become morally corrupt. In Buddhist thought, during the Age of Dharma
Decline the teachings of the Buddha will still be correct, but people
will no longer be capable of following them.</p>
</blockquote>
 362: <p>Deepangkara Buddha was born before Kondangna Buddha but the aeons between the two births are uncountable. </p>
 -1: <p>Today I found this which seems to answer this question.</p>
<blockquote>
<p><a href="https://www.accesstoinsight.org/tipitaka/sn/sn56/sn56.048.than.html" rel="nofollow noreferrer">Chiggala Sutta: The Hole</a></p>
<p>&quot;Monks, suppose that this great earth were totally covered with water, and a man were to toss a yoke with a single hole there. A wind
from the east would push it west, a wind from the west would push it
east. A wind from the north would push it south, a wind from the south
would push it north. And suppose a blind sea-turtle were there. It
would come to the surface once every one hundred years. Now what do
you think: would that blind sea-turtle, coming to the surface once
every one hundred years, stick his neck into the yoke with a single
hole?&quot;</p>
<p>&quot;It would be a sheer coincidence, lord, that the blind sea-turtle,
coming to the surface once every one hundred years, would stick his
neck into the yoke with a single hole.&quot;</p>
<p>&quot;<strong>It's likewise a sheer coincidence that one obtains the human state.
It's likewise a sheer coincidence that a Tathagata, worthy &amp; rightly
self-awakened, arises in the world.</strong> It's likewise a sheer
coincidence that a doctrine &amp; discipline expounded by a Tathagata
appears in the world. Now, this human state has been obtained. A
Tathagata, worthy &amp; rightly self-awakened, has arisen in the world. A
doctrine &amp; discipline expounded by a Tathagata appears in the world.</p>
<p>&quot;Therefore your duty is the contemplation, 'This is stress... This is
the origination of stress... This is the cessation of stress.' Your
duty is the contemplation, 'This is the path of practice leading to
the cessation of stress.'&quot;</p>
</blockquote>
 -1: <p><strong>...cosmological evolutionary occurrence?</strong></p>
<p>By 'evolutionary' if you mean a random event as like a 'random mutation in biological evolution', then NO. It's definitely a cosmological event as in, the attainment of Nirvana by a would be Buddha is a Cosmological Phenomena it's not a trivial case of altered consciousness of a Human.</p>
<p><strong>...if not, then who or what is governing these occurrences?</strong></p>
<p>There is No-Self and definitely no higher being controlling anything according to Buddhist Cosmology and Philosophy in general.</p>
<p><strong>The Occurrence of a Buddha</strong></p>
<p>It has vastly to do with two things;</p>
<ol>
<li><p>The <strong>Karma</strong> of the would be Buddha, we are all potential would be Buddhas, our individual Karma will determine who would end up being one. With each act of Kindness and each Unwholesome deed, we birth our future.</p>
</li>
<li><p>The conditions for the arrival of the Buddha should be adequate, for e.g. The Buddha would not have born in say for an e.g. ancient Egypt because people were not into meditation nor would He have found bhikkus to memorise his suttas and pass on, He would not have born in British India or the Islamic India, He will not be born in Antartic or Arctic, etc you get my point. For a Buddha to carry out His operation of teaching the Dhamma to the fellow Humans, the conditions of His arrivals have to meet a certain environment, a milieu.</p>
</li>
</ol>
<p>Finally, ponder upon this simile,</p>
<blockquote>
<p>The Buddha used a sea turtle to illustrate the precious rarity of opportunity afforded by our human birth.  The turtle example appears in the scripture called in Pali, the Chiggala Sutta that is classified as LVI.48 of the Samyutta Nikaya.</p>
<p>&quot;Monks, suppose that this great earth were totally covered with water,
and a man were to toss a yoke with a single hole there.</p>
<p>A wind from the east would push it west, a wind from the west would
push it east.  A wind from the north would push it south, a wind from
the south would push it north.</p>
<p>And suppose a blind turtle were there.  It would come to the surface
once every one hundred years.</p>
<p>Now what do you think - Would that blind turtle, coming to the surface
once every one hundred years, stick his neck into the yoke with a
single hole?&quot;</p>
<p>&quot;It would be a sheer coincidence, Lord, that the blind turtle, coming
to the   surface once every one hundred years, would stick his neck
into the yoke with a single hole.&quot;</p>
<p>&quot;It's likewise a sheer coincidence that one obtains the human state.</p>
<p>It's likewise a sheer coincidence that a Tathagata, worthy and rightly
self-awakened, arises in the world.</p>
<p>It's likewise a sheer coincidence that doctrine and discipline
expounded by a Tathagata appears in the world.</p>
<p>Now, this human state has been obtained. A Tathagata, worthy and
rightly self-awakened, has arisen in the world. A doctrine and
discipline expounded by a Tathagata appears in the world.</p>
<p>&quot;Therefore your duty is the contemplation: `This is stress . . .  .
This is the origination of stress . . .  . This is the cessation of
stress . . .  . This is the path of practice leading to the cessation
of stress.&quot;</p>
</blockquote>
