Ok hab was in der alten Nagios Doku gefunden oder besser gesagt einfach mal nach “first_notification_delay” gesucht.
The time for “first notification delay” is timed based on the last known OK state not from the first failure
So if you normally check on 5 minute intervals and recheck interval set to 3 minutes with 3 tries, the service would reach a HARD state at
5 + 3 + 3 + 3 = 14
Being you have your “first notification delay” set to 13 it would be sent immediately.
If you want the notification to go out 13 minutes after it goes into a hard state, set it to 27.
Also im Endeffekt noch etwas Rechenarbeit für dieses Setting.