At the present time there is one and only one smart app that will run locally, and then only if you are using only standard device types. That one is the new “smart lights” lighting wizard.
No other smartapps will run locally. That includes smartthings-created smartapps like the smart home monitor, and the officially published smartapps like everything in the marketplace.
And if you use a custom device type, then that particular instance of smart lights will not run locally either.
But if you have a light switch using a standard device type, smart lights will run locally. And that’s it. Much discussion of this in the forums in the V2 and the local processing topics.
We’ve been told that additional smartapps will be able to run locally eventually, but no particular timeline or process details for when or how things will get approved.
Apparently, the problem is that in order to run locally, at the present time that smartapp must be pushed out in firmware to all SmartThings V2 customers. Since everybody already gets smart lights, including any updates to it, that’s the one they picked for local operation.
I realize this doesn’t fit anyone’s expectations for what “local processing” was going to mean based on previous conversations, including conversations with SmartThings staff, but that’s what we got.
This limitation has been confirmed since the date of the release on September 3 by multiple Smartthings employees, including the CEO and the CTO. So again, check the v2 topics in the forums for additional discussion.