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First and foremost, are you practicing these skills under the supervision of a trained coach who is capable of spotting these skills?

You really need to be careful when attempting skills that involve height, rotation, and twisting.
From what you said, it sounds as though you are having difficulty adjusting for the timing difference between the trampoline and the floor.
Obviously, the trampoline has a lot more give than the floor does. This means that your skills will be much slower going into the throw.
When you transition to the floor (which does not have as much give) you need to be able to initiate the skill much quicker.
If you are coming out of a round off or roundoff, back handspring, that means you have to land the body nice and tight and slightly short of the vertical to allow the body to set in the right direction. Make sure the arms are up.
It sounds as though you are still twisting as you land. Your somi is most likely too low which can best be fixed by not whipping into the rotation. Dig in, set the chest to the ceiling, and you will have more height to finish the twist.
Keep in mind of course that these are some general ideas based on the little information that I have of your situation. Nothing can truly replace the comments of a coach who is with you during practice to actually see what is happening.
If you haven't been... make sure you get a trained spotter to help you with these skills. Play it safe. You don't want to hurt your back.
Good luck!