Is it normal to CC my professor when they introduced me to someone? Research student in Japan here.

Recently, my professor (Japanese but studied in the U.S. for  long) introduced me to his friend who was a guest lecturer. I got the guest’s contact information and communicated with him through e-mail. When I reported that at the next weekly meeting, my professor gently advised me that it is generally considered “rude” if I didn't CC my professor when I contacted someone he introduced me to.

But that confused me, because back in another university in the U.S,  when I CC’d my professor to contact another researcher, my American professor told me nicely,
“Let me give you a general advice. Professors don’t want the inbox clogged up. You generally always want to save your professor’s time. Simply report to me in our weekly meeting when there is a meaningful progress”

In both scenarios, I met the guest lecturer in person, and I was given their contact info directly from them, not through my professors.

While I will follow my current professor’s direction (to be safe), I was genuinely confused by what is the norm or standard in these situations.

Can anyone tell me what is the norm? 
I assume it is safe to CC professors from now on?
Most faculty are curious and would like to know what their students are doing, therefore you should CC them. If you CC them, they don't have to ask you if you sent the email.  If you CC them, they have the opportunity to clarify what you have written.

Some faculty consider deleting an email to be an unpleasant chore.  If your supervisor is one of those people, do not CC them.  

Otherwise it is a matter of individual preference.  Few people consider it rude to CC or rude to not CC.