Rhumba on beat1.... Well, it is different for International Latin Rhumba versus American Rhythm Rhumba. International Latin begins on the two beat and American begins on the one beat. So, I am assuming that the question involves the American version.

Then, to make it a little more confusing, there are two different methods of teaching American Rhumba. The Fred Astaire school of thought does a quick-quick-slow beat, starting with a side step (beat 1) and close on the quick-quick and a forward/backward step for the slow. The Arthur Murray school of thought does a slow-quick-quick, starting with forward/backward step on beat one (slow), followed by a side step and close for the quick-quick.