SmartThings v2 Hubs can process some automations locally:
Some preconfigured automations can run locally.
Manual, on-demand control of a device or SmartApp through the SmartThings mobile app always requires an internet connection to the cloud and cannot be performed locally.
The documentation does not list which devices in particular are able to function without access to the Internet. Since the bulbs use ZigBee, it seems logical that they should be able to run locally, but I've heard people say that they had trouble with it.
Can Philips Hue bulbs be controlled locally if the hub's connection to the Internet is lost with automations?