It’s not the device which determines whether it runs locally, it’s the device type handler. Only device type handlers created by SmartThings themselves are eligible to run locally. Any custom code will not.
There are at least two different device type handlers that should work with the Aeon siren in order to run locally. There’s no official list of these, but there is a community maintained list in the following thread
However, you will probably give up some functionality if you do go to one of the local DTHs. That’s the trade-off.
Also, remember that if the Internet is not working, the mobile app will not be able to reach your hub.
(Technically that would be possible if they were on the same Wi-Fi, but it’s just not the way smartthings has designed their platform.)
So when you set up your siren, you need to set up something else that runs locally to be able to turn it off. This is especially important because you cannot change the mode or dismiss a smart home monitor alert while running locally. The minimote is usually a good choice, but there other options as well, again, though, you have to set this up ahead of time using SmartLighting. ( routines do not run locally either.)
Anyway, as far as your question, the first issue is what device type handler are you currently using for the siren?