AlarmManager on API19 has the method setExact() to set an exact alarm.
Exact means --> If I set an alarm to 2:01 p
Using setExactAndAllowWhileIdle() for a one-time alarm will fire exactly on the given time even in Doze idle mode. So this probably is the way to go.
Problems start, if you want to repeat the alarm at a rate of < 15 min (or set any other at a time < 15 min away from the last one), as this will not work in Doze idle mode, where such alarms are forced to the next 15 min or are executed when idle maintenance starts, which happens for about ten minutes first after 1 hour, then after another 2 hours, then after another 4 hours and so on.
- EDIT -
As of today Nov 17, Dianne Hackborn writes in this Post's comments: "For what it's worth, the minimum time between while idle alarms will be changing to 9 minutes at some point relatively soon (even on devices running the current Marshmallow builds)."
This doesn't change anything fundamentally though.