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The reason you can't move any touching balls that are in contact with the cue ball is because it is a push shot so ALL balls that are touching the cue ball should stay perfectly still when it is played.

If the contact is with a ball of your target colour then the shot starts with that box ticked (just like the point where the cue ball makes contact in a normal shot). Once you've made contact with a ball of your colour the cue ball can hit any ball.