What could cause a rear twin-jet's throttle to oscillate on descent?
I think your note about this taking place in the Atlanta area with heavy Cumulus clouds in the area is the best clue as to why such large throttle inputs were necessary.  It sounds like there were thunderstorms in the area in the cumulus and mature stages.  The pilot was most likely encountering heavy updrafts and downdrafts passing through the air and had to compensate accordingly with the power levers to maintain approach airspeed and glidepath during the approach.