Explanation:
The trampoline is more like a net than a solid surface, very little air resistance on the trampoline mat, so there's not much loss in energy during a bounce. The old competition canvas type trampolines used 1/4 inch straps with 5/8 inch or larger "holes". Current versions of competition tramps are more net like, often called "ozzie" (Australian) trampolines (although some brands falsely claim to be "ozzie" like).
During the actual bounce on the trampoline surface, the bouncers are contracting and extending their legs to add energy to each bounce. Leg extension is done near max g force on the trampoline, which is how work is performed to regain energy. The increase in energy from leg movement during a bounce is more the enough to compensate for energy losses.
Note that the goal in the video is to "stick" the landing, not to maximize height from the bounce, so the bouncers are only trying to add just enough energy (with leg movement during bounce) to have a clean landing back on the platform.
With these efficient net like trampolines, you can start by lying flat on your back, then use leg motions to initiate movement, and continue to land flat on your back, using leg movement to increase the height of each bounce, eventually reaching a point that a bouncer can start doing a flip between each bounce and continue to gain height until reaching some limit.
Note that landing off center on competition type trampolines doesn't perceptibly bounce a person back towards the center. It doesn't take any noticeable change in method to bounce vertically while bouncing quite a bit off center, and in the video, some of the bouncers land in the center of the trampoline and still return to the platform. This is because they use the extend their legs a bit backwards during the bounce to end up back on the platform, combined with contacting the trampoline surface a bit short of perfectly flat rotation so that the bouncer "rolls" backwards during the bounce to end up back on the platform.
This example during a practice shows more variations that what is used during actual performance. At 1:50 into the video, you can see the "reverse" bounce seen in the OP's video. Also you can see the bouncers can't quite return to the top of this particular wall (it's taller than the one in OP's video), but can return to the highest extended ledge. At 2:44 into the video, you can see the net like surface of the trampoline.