Anyone with the Administrator flag set will get system alarms in the local system, that is just the way the system works.
The "Broadcast System Alarms" flag controls whether or not system alarms are broadcast to the network so that administrators on other systems in the network get alarms for remote systems, it has nothing to do with local alarms. There is no way to turn off system alarm messages without disabling the Administrator flag that I am aware of.
Note that if the main alarm you get is the Insufficient Bandwidth alarm, that can be disabled in System Flags, otherwise there isn't much you can do.