The force at which the kid hits the trampoline decides the force at which it throws him up. If the kid were to lightly bounce, he would get little force from the trampoline. Because the kid is putting a lot of force into the trampoline, it returns him with enough force for him to get a backflip.
A bouncy ball works like a trampoline. If you drop the ball, it will get little height. The closer you are to the ground, the less height you will get. A six foot tall man throwing the ball at the ground with all his force will make the ball go higher than a little boy doing it. In this picture the two balls at the top were dropped from higher than the ones below.