Everything @ogiewon said with one tiny addition…
It’s definitely true that almost everything runs in the cloud, not on the phone and not on the hub. The hub is basically a box of radios just used to communicate with the local devices. But the hub sends those communications based on logic in the cloud. And when it receives those communications it send them on up to the cloud for processing.
It does sometimes happen that the cloud account and the hub get out of sync on the status of some devices. It shouldn’t happen, but it does. So rebooting the hub will cause it to resync the current status of everything from the cloud account. That does sometimes “unstick” the presence indication for the phone being used as presence.
So rebooting the hub can sometimes, but rarely, help when the problem is the phone showing as away when it’s home or showing as Home when it’s away. If it’s not disruptive, it’s one of those “can’t hurt, might help” things.
But it’s not helping for the reason you might typically think, which is that you’re clearing the cache for something that runs on the hub. Because hardly anything runs on the hub. But it will re-sync the hub and the cloud account, and sometimes that’s useful.