I'm a lawyer & my office does bankruptcy.
It's because kids change majors (which may mean a tuition differential), add classes, drop classes, go to part time, or decide not to attend at all.
Does the school website have an online calendar of Important Dates or something similar? That usually mentions payment due dates.
It also sounds odd to me that they don't want the money in advance, although it makes sense that they wouldn't want to deal with making refunds. When my dd was in college 5-10 yrs ago we had to pay each term's fees about a month before classes started.