I don't know what you mean by snap them onto my head. I do as I do with all my headphones, I take them off their stand, widen them enough to pull them down over my ears and then move them into place on my head. As for pressing them on, I'm not sure what this means either, but there's a power button on the side, which I obviously have to press to turn them on, off and to search BT devices, but other than that, there's no pressing on them.
Could I have damaged them by just switching them on? Seems unlikely, unless this is a weird design flaw. @Audeze is this possible?
By 'snap them on', I mean instead of gently placing them on your head, you let the earcups go so they 'snap' on your head. By 'press', think of when you're bored and you place your head on your head, it's like that. Or even if you feel like the seal around your ear is loose, so you press the earcup against your ear. That kind of thing could change pressure (if I understand it correctly) and damage the diaphragm. Audeze have amazing customer support; should definitely get in contact with them about this.