My Instructors teach to dance the one beat, hold for two, then quick quick for 3 and 4

and then it is the bending of the knees which gives the "hip" action or "Cuban motion"

we land on the one and the feet stay in place but with the "and-two-and" our leg is straightening-weight shifting-right knee bending

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.