God, Neji is 17 at best, why the hell would he have students?
not every jounin has students, not all jounins are fit to be teachers...
the way i see it, all the jounin teachers were past their prime, or at least past thier growth period. it would be a waste so send someone that has the poteintial to exceed every hyuga in the past few years to teach some kids who are still wet behined the ears.

and as for team kakashi, of course, Kakashi is still the team leader during missions, and still has whatever privilliges as a jounin over genins and chunins, but he does not have the authoriry to order them to train at something or whatever, it's like how the realtionship was between Shikamaru and the genins before.