I’m glad to announce that I finally found reliable solution for proper work of Nights Keeper on Android 5 devices. The only restriction is that Alarms will be silenced during profile work. So, you should set Alarm and profile time with this in mind. And you need to accept the access to notification for proper work.
I’ve just released new version only for beta testing (want to check everything once more before public release). So, if you are Android 5 user and want to take a part in this beta testing you are welcome. Just follow this instruction to become beta tester.