Which monitoring service are you talking about?
If you are talking about the built in one that sends messages like:
As far as I know this only triggers when an individual service stops working or is shut down.
Jul 20 17:42:55 email zimbramon: 5289:err: Service status change: email.pyxislab.com antivirus changed from running to stopped
I know that, at least on my setup, zmcontrol stop and zmcontrol start do not send these messages.
So my guess would be that you need to make sure that your backup method uses zmcontrol start/stop, or if it does use this method to shut down then do you have some external monitoring service that is sending these messages?
As for disabling a service so it wont start up in the administration console go to servers-> server name-> services tab.