Popping out won't be a problem, but "half-contact" will be. If the power-up ramp is not controlled, at least the Xilinx chip may suffer a latch-up (i.e. "dies"), essentially causing a short on the 3.3V rail. So you should really make sure that it does not pop out. I've watched your video, and it does indeed clip down nicely, so I would not expect what I see next in that video.
One more thing you could try is to clean the Lisa and the socket with alcohol and an old toothbrush. This "easy popping back" does seem like there's some kind of grease on the pins (did you use a contact spray on this chip?), making it way too easy for the socket to be moved. With pure alcohol and a toothbrush, you will remove any such layer, and it may hold good enough for stable operation.