Part of the “lag” problem has to do with the fact that the Touched event is bad at responding to Humanoids. When you land on a part, the Touched event will not fire until the character finishes “landing” and settles after a moment. The FloorMaterial property of the Humanoid does update instantly, though, so you can work around the broken Touched behavior with an ugly hack by listening for the FloorMaterial to change from Air. The only other problem here is that a JumpPower of 10 isn’t high enough for the FloorMaterial to change, so really it’s going to require a precise calculation to determine when the character should land given how high they last jumped, and a raycast to check if the character is landing on the trampoline part.
This would be much easier if the Touched event just responded properly to jumping humanoids.
an additional workaround would be to place an invisible, non-colliding “hitbox” part above the trampoline, so then the legs will make contact with it immediately and fire the Touched event instead of the humanoid stopping and hovering over it for a bit.