The screen on my phone turns on when the battery is 100% charged... I would also like to be able to disable that feature but haven't found a method to yet.
Once I turn the screen off however, it does not come back on again while the battery is at 100%. Presumably, if the phone went below 100% and/or started charging again it would go back up to 100% and the screen would turn on again, so something to check--if you use a charging cable instead of a dock--make sure the USB connector is not old or bad (i.e., intermittent).
If the USB connector doesn't make good contact then the phone's charging logic can be re-triggered and the screen will come back on. You can see the effects of this yourself by plugging and unplugging the charger. The display may come on briefly, turn off briefly, then turn back on again to say that it's fully charged, and a cheap USB cable that wears out can eventually cause this to happen repeatedly.
I don't think this is the issue you're having based on the symptoms described, but something to look at. Another possibility would be a sub-standard charger and/or heavy processor usage on the phone that allows the battery to be charged but then discharged enough while it's still plugged in so that the phone thinks it needs to start charging again. I'm not sure if that can actually happen or not, but if the phone thinks it's time to charge the battery again, and then it charges to 100% almost immediately, you will get another notification with the screen turning on.