Yeah. You are putting too much work into the twisting as you leave the bed (or floor) and so you are leaning into it. That makes you go off balance. You have to focus less on the twist and more on jumping up keeping your body straight and tight. The twist part doesn't take that much work, the key is to keep your body straight and tight with your arms up or in so that your mass is all concentrated close to the axis of rotation. Then you twist easily. It is even easier if you start with your arms stuck at the sides in a T shape and then pull them in. Also Devon is quite right. There's no point in trying to do a full twist jump if can't do a half-twist jump with good control. Start small and build up. Pick a point in front of you to focus on as you jump up, then look over your shoulder for the twist.
Honestly, you could probably just practice jumping in a 90 degree angle, and work your way up from there, and I have had this problem as a kid, i guess it just went away for me, I can do a 720 just fine, so i guess just practice jumping and work your way up to spins.
Your core might need strengthening. This website is a beginning to total fitness. It tells you which muscle groups to work on. good luck.
http://www.fitstep.com/Advanced/Anatomy/...
You are obviously shifting an uneven amount of weight to one side. watch professional iceskaters and use their form