Final exams: What is the most common protocol for scheduling?

In the two major US state universities that I have either been a student or taught in, the process was roughly the same:

Final exam times were based on the first day of the week course time for the main course meeting, typically a 'lecture' section. Every course that started at 9am on a Monday had the same final exam time. Every course that started at 11am on a Tuesday had the same final exam time. All these decisions were made centrally.

The exam times were mostly unrelated to the actual course times, since the final exam slots were longer than the actual class meetings, but it ensured that no one had overlapping final times because no students would have two courses that met at the same time. The exception was courses that were specifically night courses, which also had night finals, with the assumption that some proportion of the students in those courses were not full-time students and may have had other daytime responsibilities.

I believe there were procedures to allow for simultaneous finals for courses with multiple sections, but I am less familiar with how those processes worked; I believe the centralized time was chosen and then arrangements were made for the small number of students for which there was a conflict.

There were also processes for students who ended up with >2 finals in the same day to make alternative arrangements, but again, these circumstances happened rarely, especially because not ever course actually utilized their final exam slot as anything but a due date for a paper/project/etc.

Both models you describe, a finals period with longer timeslots which is coordinated by the school and having finals during ordinary class periods, seem to be commonly used at schools in the US but it appears that which is used depends a lot on (for lack of a better word) the level of the school. The former schedule is dominant (and perhaps universal) at state flagships, top research schools, and elite liberal arts colleges. Both schedules seem to be common at community colleges. I don't have access to good statistics, but it's plausible that the latter schedule is the most common one at community colleges (which would explain your administration's explanation).

I'd speculate that one reason is that community college classes tend to have many shorter exams throughout the semester rather than a single final worth a large percentage of the grade. (Of course, this means it's a terrible idea to switch systems during the middle of the semester, but it might suggest an alternative for future semesters.)