There are 3 main ways to twist in trampolining and 3 more that are used by self taught trampolinist.
The main twist used by beginners is the off the bed twist initiated by turning the shoulders as the trampolinist leaves the bed. This is best taught by teaching the trampolinist to look where they are going.
The next twist, taught at the stage of twisting in single somersaults and twists from back landing, is an aerial twist initiated in shape by shoulder turn and accelerated through straightening the shape.
The third method of twisting, is the tilt twist, used for twists from multiple somersaults. This is initiated by extending the arm and allowing gravity to cause the body to rotate towards the new centre of mass, before accelerating the speed of turn by moving the arm back into the side of the body.
The other 3 methods of twisting are 1. hip twisting which can be diagnosed by the arm moving slant ways across the body. This will always cause the trampolinist to struggle to attain more than 180 degrees. 2. Leg scissors ( sometimes seem in cat twist) and 3. Eccentric force from one arm pushing into the trampoline as the trampolinist is on the takeoff phase. This is often used for half twist from front landing and for cork screw ( 1 1/2 twist from back landing to back landing)