I'll give you the band version that I heard. Dr. Julian decided that the song fit perfectly in his famous "Circle Drill" and became a fan favorite in 1972. If you know the style of songs that are usually played in the circle drill, it is at a convenient tempo of many songs still (occasionally) used by Dr. Sousa.
UT had played it in the half time shows but not like we know it played today.
I know that in the mid to late 70s when I was becoming old enough to start following football, you almost never heard the band play "Rocky Top" like you hear it now. It was always "Down the Field" after touchdowns and such. Anyone know when the band started playing it so, uh, incessantly?