I have since removed the tab from the 360 case and put it back in the clip case. The issue seems to slowly get better. The newton rings have now disappeared and only rarely appear when I take the tab out of my bag. But they disappear on their own after a few seconds without me having to push on the back of the device. Yesterday, when I first noticed the rings, I was able to "control" them. I found out where/how to hold the device to make them disappear and where to push to make them re-appear. The later now no longer works, they appear shortly but disappear on their own.
I assume that the case I got (while not technically broken), seems to be a little bit too tight for the tab. Might be a rare situation, though as a lot of other people don't have any issues with it.
anyways, back to my clip case. phew :)
Phone: Nokia Lumia 920, retired my HTC 7 Mozart
Tablet: Acer Iconia W510 (Windows 8 Pro) - finally got rid of the horrible Samsung Galaxy Tab (P7510)