They do. You can visit others' Domains, though some people guard them or redirect visitors somehow, if they really don't want anyone to poke around in there while they're gone. You have a level of control over your space even if you aren't here.

[ Ciri leads Kelpie to the water, and the mare doesn't seem too annoyed by the goats, mostly just ignoring them. In the Horizon, Ciri doesn't even need to bridle her horse to ride her, so Kelpie is wearing only a very basic, light saddle and a halter. She could probably use nothing but her will, but it doesn't feel natural. Either way, Ciri just takes off her halter and lets Keplie loose to drink and graze, knowing she won't wander far.

Sypha's assessment of unicorns gets a look from Ciri and a bit of a nod. ]

I made her. Same as everything.