Android lights up when charged

Samsung Galaxy S5 turns on when fully charged and never turns off

I just 'upgraded' from the Samsung Galaxy S4 to the S5. Both use similar 4.4.2 Touchwiz software, but by new one has some odd behavior. I'll explain. Notes: I set smart screen sleep (or timeout, how it's called) to ON and put it to one minute. I do have the Dev options revealed, but the "Stay awake" is not checked. I'll describe some situations:

Phone unplugged, unlocked -> Sleeps after 1 minute idle. Phone unplugged, locked -> Sleeps after 1 minute (or even less) idle, no matter if I have notifications or no. Phone plugged in, unlocked -> Sleeps after 1 minute idle. Phone plugged in, locked, manually woken up (pressing some button) -> Sleeps after one minute. Phone plugged in, locked, woken up by some notification -> Rings, displays the notification, and never sleeps until I press the lock / power button.

I tried to minimize the problem by minimizing the notifications I get while it sleeps: turned off wifi, blocked messages, etc. But there is still one problem. I charge my phone over night. Plug it in at evening (22:00), at about 1:00 (night) it finishes charging. The "Battery full" notification appears, and also the popup saying "Close the charging cover for water protection" fires up. And after that, the phone does not time out. And when I wake up, the phone is very hot. I bet it's not OK. And also, from my knowledge, static images burn into OLED displays. I really don't wanna break my phone by charging it at night.

What I tried: restoring and leaving dev mode off. Resetting to factory, twice. Tried letting it on silent with and without vibrate. Tried putting some apps to block notifications, tried changing all the power, timeout and sensors options. Nothing stops it from lighting up and never lighting down at night, and over-heating itself. Any ideas?