Being the last author as an undergrad TA (a PhD student) of one of my classes was looking for an undergrad to join in one of his projects. This was not directly related to the field I want to work in grad school, but there is no group or faculty in my preferred area, so I wanted to join in anyways (because it is another area I enjoy and I had lots of free time). We started working on it with him, had weekly meetings, I helped with theoretical aspects, and I did all implementations (replicating the other papers that did not provide code so we can compare plus our own experiments). I also did a lot about designing the experiments (which is the only way of proving your work in this area).

This got accepted to one of the top conferences. While I obviously didn't expect to be the first author, I was kind of suprised when I saw that I was the last author, and the professor (PhD student's advisor) was the second last author. For context, it is CS (but not theory), and the author list in our paper is clearly not alphabetical. Now, my questions:


Isn't this unusual? I thought it was better for a professor to be the last author? When I asked the PhD student about, he just said it was the professor's decision.
Should I still include this in my PhD applications (it's my only publication so far)? I feel like the admissions committee would ask about why I am the last author.
When asked, should I mention the possible reasons? I never asked the professor, because, after this project, the PhD student left the program and started a PhD program from scratch somewhere else. Since I had mainly worked with him, and since it was not my primary interest area, I decided to not start a new project. (I don't remember if I conveyed this to the professor after the author list was sent or before, it might have had an effect). 


Finally, I have checked this professor's Google Scholar page, and in fact he has acted similarly at least 3 times before (3 publications, each with some of his PhD students, in each one, one of the PhD students is the last author). I believe this (and his other PhD student leaving) are supporting facts for me, I still feel like it could come across as whiny
There are at least three basic author order schemes:

1) Alphabetical

2) In decreasing order of contribution

3) Split into junior and senior contributors, with juniors coming first in decreasing order of contribution, and then seniors in increasing order of contribution. [Often with just one senior spot]

In Computer Science, I've predominantly seen 1) and 2). An undergrad being at the end of an author list that is clearly not alphabetically ordered is a dead give-away for order type 2), and hence does not require particularly explanation.