As far as having an intrusion run a routine, you can certainly do that. You just don’t do it with SHM.
Instead, have the exact same event that triggers the intrusion run your routine. Easiest way to do this is by creating a virtual switch and then having that switch turning on run your routine. There is already a smartapp in the marketplace that can tie a routine to a virtual switch. This has been around for a long time and is very popular. In fact it’s so old that it uses even older terminology, “home phrase,” instead of “routine,” but they mean the same thing.
This is the same way that people create an echo voice command to change a mode and smart things. So you can just read through the FAQ for that and you’ll see how it’s done.
Also know that if you want to be able to run a routine with one tap you can set it up as a widget on a smart watch or your phone. That can be useful for some routines.
https://support.smartthings.com/hc/en-gb/articles/206145893-Is-there-a-SmartThings-widget-
It was a little difficult for me to follow your post because I think you were using “mode” when you meant “alarm state,” but I wasn’t sure. It could’ve gone either way. But in any case, you should be able to get the routines to occur automatically, just perhaps a little differently than you thought.
Finally, if what you really want is that when you manually change the alarm state you want to have a set of routines run, that can be done with core. Core is a community created rules engine, very sophisticated, but pretty complex to set up. If that’s the use case that you need, let us know and we can point you to the information on core.