It may seem pedantic, but in these matters, it is very important to keep the terms straight.
Every student athlete who ever worked a part-time job while in school was an employee. But not of the University of Tennessee. If they washed cars for the Ford place, they were employed by Ford. Now, with NIL, they can be paid for their fame. Before, they couldn't. Now they can. So now maybe their employer is Spyre, and they're being paid to autograph stuff, to attend social gatherings with fans, and so on. But it's really no different from when they used to wash cars for the car dealer, just now they can be paid explicitly for the fame that goes with being who they are (college football players).
Out of all of that, the important thing to keep in mind in answering your question is: they are NOT employees of the University of Tennessee. As far as UT is concerned, they are students...student athletes. They do not have a "job." They have responsibilities that go with (a) being a student at the University, and (b) being an athlete in one of the sports programs, and maybe also (c) being the recipient of a scholarship. So lots of rules and responsibilities as student-athletes, but no job.
So there you go. They are employees in one part of their lives, and student-athletes in another part. They have to do all those things the right way. Just as student-athletes with part-time jobs have been doing since time immemorial.