Twist refers to a rotation of Nage's forearm. This twist occurs at the beginning of contact with the partner. If Nage's wrist is grasped the twist occurs as soon as Nage starts moving after the grab. This applies to irimi and tenkan.
In the initial part of tenshim on the step back relax the shoulder so that the arm is like a rope. With the initial movement the grasped arm will tend to come up into a straight line with Uke's shoulder. If Uke is holding the arm down this lifts Uke's center making movement much easier. The forearm twist comes as Uke's arm is cut down.