That really depends on personal preference. From my perspective, you move back, when the opponent is ahead on timing/takes you by surprise. You stay static/either don't move or sidestep when both you and your opponent have the same timing, and you move forward when you're ahead on timing. I learned that initially with weapons, but feel it works perfectly with no weapons as well.I assume you are talking about to push with your left hand, and punch with your right hand at the same time.
When you punch, your opponent's body can
1. move back,
2. static,
3. move forward.
IMO, for your striking result,
1 < 2 < 3
MT guys like to pull their opponents into their knee strike. The head-on collision always cause more body injury.
A + B > A
For the result you state, I think it depends on the situation. If they don't manage to dodge your attack, then your assumption of 1<2<3 is right. But if they manage to dodge, then 3 is probably the worst option. You never want them to dodge while coming in, if you punch. That results in their punching having the force of their punch + the force of your punch, which is not fun at all. Ideally, if I punch, whether or not their responding, I want them moving back as it allows me to chase for 1-2 more strikes before I back out and reset.