It isnt about off contact/pressure adjustment when it comes to something like this using a single transfer and pressing. All of your ink is being printed onto a piece of paper and that paper is flat. Then, you are pressing that already flat film of ink using a giant flat piece of metal and that metal must contact the whole image to properly transfer. The only way to then have certain areas raise would either be to do separate transfers layered with different off contact/pressure settings, or some kind of puff in one of the colors that you then heated up after the initial pressing and removal of the paper, though I don't think it would work terribly well, or at least the effect would be muted much more than direct printing with a puff ink.
edit: From what I have seen of puff foil like you described (only online admittedly), you are pressing the foil, then doing a second heating either with no pressure (heating element hovering) or back through a dryer, which lets the ink puff after the foil has been pressed.