By nature, Tyson isn’t particularly territorial. He will allow people into his spaces without much fuss, because Tyson is confident that he can defend his home and the people that he cares about.
He remains cautious and watchful for any danger once people get close, and understandable paranoia causes regular patrols to ensure his safety, but that simply means that Tyson remains on guard - just in case - rather than trying to keep people out of his spaces or away from his things.
However, Tyson can easily be unnerved by taking away the things that are his.
It will set him on edge for hours, even the slightest action. Taking his established seat in a room will have him on the back foot immediately. Taking away Tyson’s rucksack will instantaneously activate his fight or flight instinct, and calling it yours will have his teeth bared for a fight.
This doesn’t apply to people that he’s already accepted, for the most part. He won’t bat an eye if his brother or family, in general, taking things, even straight from his hands, nor will Tyson care about the Moriarty Mirrors playing with his things. Sebastian will provoke a stronger reaction from Tyson, especially if its related to the web, but he is still oddly okay with Moran taking his things.