Note: The "light up on notification" concept only works when your phone is idle or not being used. The case will continue to light on when your phone's screen is on.
If the case light doesn't turn off after 1-2 minutes, follow the steps provided to fix the issue. (If step 1 does not fix the problem, move on to step 2);
Turn off "Raise to Wake"
You can turn this setting off by the following route;
Settings -> Display & Brightness -> Raise to Wake
Close all apps that are running in the background.
Turn off your bluetooth.