At the risk of being a killjoy and / or starting a flame war, IMHO using a rebounder for a workout routine that was produced on a firm floor surface is a manifestly unsafe thing to do, especially barefoot.
Although I've never trained on a rebounder before, it should be noted that in all of the rebounding classes I've ever seen all participants and instructors are wearing proper footwear, and the bpms are pitched so that movements can be executed safely and with good form given the more unstable surface and limited surface area of the rebounder.
Cathe's workouts are produced very carefully, and it is incredibly risky to so radically change a fundamental element of her routines as the impact-bearing surface on which you are exercising. There is an inherent risk to any high-intensity workout; however, the risks involved in performing a workout routine on a rebounder that was not specifically produced for that piece of equipment are far greater than the possible rewards.
A-Jock