The general guideline for tightening QR skewers is that you should need to use the frame or fork or the body of the trainer to tighten them.
I used to store my bike in an upright position on my trainer (in the case of the Tacx Flux it actually was definitely wearing on my dropouts). I think the sloppy adapters might be causing some noise that didn’t occur when I have used other trainers. It also causes some ambiguity regarding frame alignment.
A bike in a trainer is going to move and flex to some degree or another, but most of the movement is the trainer flexing or moving on your trainer mat, I think.