Oh, yeah, I looooove this. 
thanks a lot, @jkp .
OK, first things first, as @jkp mentioned, smartthings home monitor and smart home monitor are two completely different pieces of code.
FAQ: SHM and STHM are different
Next, regardless of whether it’s SHM or STHM, only some of the automations are eligible to run locally.
If it’s a custom automation, it won’t run locally. It has to be one of the standard alerts.
You can go ahead and contact support, if you like, because they can see more things from their side.
https://support.smartthings.com/hc/en-us
If you’d like us to continue helping you here, we’ll need to see screenshots of exactly what you have set up for the automation.
Also, just to get this out-of-the-way, you cannot change the security arm to state or the location mode unless the smartthings cloud is available. So you would have to have the system armed before you unplug the router. And you won’t be able to turn the siren off or disarm it until you get the router back up, so be prepared for that.