When you changed and started punching you likely were timing the shot for the release to go off at exactly the right time. When a timer is "on", he is nearly unbeatable. But when he is "off", he becomes very eratic and can't hit anything. If he keeps it up, he will usually develop target panic bad enough to make him quit archery.
There are a couple of pros who can do it, but 99% of us can't.
For most of us neither punching or squeezing with our fingers is the answer. Best accuracy is achieved by setting our trigger finger like an unmoving steel hook and using our back muscles to pull through. The visualization that most use is trying to hit the wall behind us with our elbow. Keep the direction of the pull in line with the arrow and the target. And use your shoulder muscles as little as possible.
Allen