Okay, David was right. The PRNGs in numpy work correctly. Throughout every minimal example I created, they worked as they are supposed to.
My problem was a different one, but finally I solved it. Do never loop over a dictionary within a deterministic algorithm. It seems that Python orders the items arbitrarily when calling the .item() function for getting in iterator.
So I am not that disappointed that this was this kind of error, because it is a useful reminder of what to think about when trying to do reproducible simulations.