This is such an important question which is never really touched upon..
How you hold the release aid is going to affect how you anchor, i.e how your hand interacts with your jaw line.
Also it is going to affect how well you can execute the trigger, so it’s going to be the difference between punching and not punching and so at the end of the day this is a fundamentally important aspect of shooting a compound.
So what is the right way to hold a release aid?
It wants to be held in such a way that the fingers stay flat and in line with the top of the hand. Many novices hold the release aid in a fist, i.e they curl their fingers so they are out of line with the rest of the hand. This is going to cause a lot of issues but mainly its going to make it easier for the individual to alter the pressure across their fingers as they draw and then execute the shot and this is the biggest cause of inconsistency that we see. If you move your fingers or if you even just alter the pressure on your fingers so that the release aid balance changes you cannot get a consistent execution. You will see that if people make a fist it is unstable during the drawing of the bow but also even when it is not totally visible this instability shows in a lack of consistency in getting ones thumb (or finger) on the trigger leading to an inconsistency of execution, which leads to questions of punching.
Rather than focus on this consistent hand position or finger position on the release aid many people buy lots of release aids until they find one that fits. This is not the ideal way of achieving a consistent finger position on a release aid and doesn’t really cure the problem because if one is not aware of what is the right position then slowly over time even with a release aid that fits one can drift into problems. With the cost of a release aid this can be an expensive way of trying to get over a problem.
So we start to see why the evolution release aids have been so successful. Due to the lack of a movement of the thumb onto the trigger to execute there tends to be a reduction of hand movement during drawing and therefore a greater consistency of hand position and a perceived better execution. Although that is a little simplistic the “true back tension” release aids have their place.
Now, the hinge release opens up all sorts of issues if used poorly. The hinge release which for years was meant to be the release aid that cured punching is misused by such a large number of archers. In order to draw the bow safely they put their hand in a position where they know the release aid cant go off, meaning that there is movement of the hand and of the release aid before execution. This technique may be seen in archers such as Jamie Van Natta where this movement is very pronounced, they move their hand into a position once they anchor, from which there is no further movement, but this is difficult to learn and control. So is possibly not the best way forward.
You are looking for the hand and fingers to form a hook around the release aid and then once the pressure is put on to draw the bow they should not move again at all.
If you do this and keep the fingers flat with respect to the knuckles then you will get a consistent anchor position and if you have made this a stable position you can move your thumb onto the trigger without issue and you will get a clean execution.