I use to love tumbling on grass, but back then I would tumble on anything.
I like some of the posts above but would like to comment a little on the "snap down". Too often athletes and coaches focus too much on the legs and forget that the snap down ultimately should be done with a relatively straight body. As the feet come down to land slightly in front of the body, the upper body should be lifting at the same time. You also have a timing issue to consider. The legs should come together slightly past vertical by squeezing the hamstrings together and that squeeze should happen at the same time the athlete is pushing off the floor with their hands. This timing really helps the RO finish with the athlete standing tall with the feet slightly in front. Last, the push off the floor with the hands should be in the direction away from the athlete, not down and/or toward the athlete. The push away will help finish the RO standing up, and the push down and/or toward the athlete will cause a delay (or dragging) of the hands. This can cause the athlete to finish bent over, piked, or what ever you want to call it. Finishing that way can cause a short or undercut back handspring. I have corrected many ROs simply by explaining the timing and the push off and the results happened immediately.
I agree with CoachTodd that the RO is one of the hardest skill to do properly and it will cause problems even two skills further down the pass after the RO.
Good Luck1