The bow doesn't pivot because the limb timing balance are timed right from the very first pull on the tree. If it wasn't balanced the bow would pivot on the cradle even when clamped down. I only need to pull the tree rope a couple inches and I can see which limb is stronger and I address that "right away" till the rope tracks the line. I can leave the clamp off and the bow doesn't pivot. I just clamp it incase I would bump the bow and knock it off the cradle.
Another thing you need to consider is when your bow is done and you are shooting, the nocking point on the string is usually 1/2" + or - a tad to get good arrow flight. I shoot 3 fingers under and my nocking point is usually 5/8th above the shelf on all my bows, even glass recurves. So I set the tree up taking the 5/8th higher nocking point on the string into consideration. And I place the nocking point at 5/8th high when the bow is all done.. When I shoot my BBO bows my palm is pretty much flat on the grip with a tad more pressure at the shelf. When I shoot my recurves and they have more of a pistol grip, I hold the bow with my thumb and fore finger and let my other finger's hang free and the pull weight of the bow is all in the web between my thumb and fore finger. I have a wrist strap on my recurve and I just let the bow pivot forward after I shoot.