Why would Earth-Prime Wells do that? He, like his Earth-1 counterpart, was killed by Thawne before the place was even built.
I'm betting that he's not going to be malicious, but he doesn't know Barry (presumably, unless some weird thing happens with Thawnes or the other Wells memories). He'll just see a group of people who from his perspective are squatting in his lab, and he'llwant his stuff back. Eventually it will be resolved, but it will be very annoying.
More likely we'll have Wells attempting to cope with everything that's happened. Like him being killed, his wife being killed, his murderer running around pretending to be him, everything being wiped from existence, everything being recreated, and his resurrection.
That will probably happen, and thats the interesting part of the character. But, unless something weird happens, he'll have no idea who any of Team Flash is, he'll just know that Star Labs is his place, and he'll probably want it back. Now, if he isn't officially declared living again he might not be able to legally take it from barry, but I foresee drama related to the Lab, which I don't want to happen but can't see it not being brought up.
Then stop watching.
Nope. Season 5 was good before the Mirror Master plot started wearing out its welcome near the end, and the show is still nowhere near as bad as it was in season 4. No shitty Thinker, no fake elongated Man taking up screentime. The show has fallen from where it was in the first three seasons, but its still very good when it tries to be and I'm sure that Mirror Master will be done soon, I don't think that it was even supposed to be in this season at all anyway, but the last part of the story got pushed because of the pandemic.