To be clear, that's only the case for certain prepositions (here's a list); most prepositions strictly take either dative or accusative regardless of motion/action. "Auf" is indeed on the list, though, so case switching does apply here.
You only use accusative when there's motion/action to or away from the noun; if there's motion, but it's remaining at the location of the noun, just use dative.
It's the same as the difference between "on" (or "in") and "onto" (or "into"). In this exercise, "we" are not jumping onto the bed (toward the bed; previously off of the bed and now on it); "we" are already on the bed and are jumping on it, staying on the bed.
- "We are jumping onto the bed" = "... auf das Bett"
- "We are jumping on the bed" (on top of it) = "... auf dem Bett"