After some time with the update I can say that it seems sometimes that the Power button does not turn off the screen. It just gets the phone to the "unlock" screen. Then you have to press the Power button again and maybe you will get lucky. Even then, the screen may turn on automatically.
Moreover, even if it indeed the phone screen goes off after pressing the Power button, sometimes if you touch the screen or even if you move the phone (!!) the screen turns on again.
It's like the phone is not really "hibernating" at the moment, but just has the screen turned off and everything else is still working.
I can't explain it any better than that.