Ujio,
If you are doing it correctly, the string and string hand do not move on your face. If you are "twisting" your face, you are using arm rather than back tension. The "pulling" with the back will move your string shoulder back, perpendicular to the arrow line, not back inline from the target/ arrow line.
Once you have your "anchor" position set, further back tension DOES NOT move the hand on the face!