The pickups are cast in polyurethane, which is also not thermoplastic. It does however exhibit another property of many plastics: creep. That's what you're seeing in response to pressure, it slowly deforms. Jimmy is right that if you reverse the mounting, it will encourage the creep in the other direction. If you leave it unmounted, there is no motivation for it to return to where it was, since it's not elastic.
Those pickups look like they've had a rough life. The top picture it seems it's already been broken, the flange looks cracked on the left edge and the mounting screw hole looks less than complete.
You only have to tighten the screws to be snug - this is a good example of one of the reasons to not overtighten the mounting. But of course the good news is that they still function.