I don't remember anything about their band from that game, except that they were there, as most visiting bands seemed to make the trip to ND. (Miami's stood out as one that never came, at least not to any game I remember.)
I also have seen footage from earlier Tennessee games and there was no "Rocky Top" to be heard. But they sure as hell played it when they returned to ND in 1991.
EDIT: Per Wikipedia, "Rocky Top" was first recorded by the Osborne Brothers in 1967 and first played by the UT band in 1972 at a game versus Alabama. It became an official Tennessee state song in 1982, so it seems likely the UT band began playing it incessantly shortly after that. At least it's catchier than USC's infamous "Only Song You Know."