I don’t think many people would trim excess immediately after they just wet out the part? Probably what you’ve seen is a green trim, once the resin gets to “B-stage” and it starts to tack up. At this stage your overlay shouldn’t lift away from the part (but of course you should be careful how you handle it so it doesn’t lift as well), but it will be much easier and quicker to trim compared to when it’s fully cured.
I don’t have any experience with overlays, but if you prepare the part surface properly I don’t think there would be any problems with the resin (presumably epoxy?) adhering to the part. You probably don’t need the mechanical grip that wrapping around the back of the part would provide.