Here are a couple of drills you can do:
Front tuck: off a tall spotting block and onto an 8-inch mat, do a standing front tuck. Be sure when you begin you stand tall with your shoulders and your hips open. When you go into your front tuck, snap your body from the tight arch position into your tuck position without dropping your chest. Land on the 8-incher. This will help give you the timing for a good running front tuck on the floor.
Back tuck: on the trampoline, bounce small with your arms straight up. As you set into your back tuck, open your hips slightly at the same time you squeeze your butt. Keep your shoulders open and bring your knees up to your tuck position at the top of your set. There's no need to grab your knees on your back tuck if you open your hips.
Hope this helps!