It’s quite possible it’s not literally his room, since we’re not actually told it is!
But I took it as being that way because it’s hard to imagine what other purpose it’s supposed to have.
We know it’s definitely not a part of that common area, because by the end of that fight we’ve seen every angle of it and nothing like Vision’s little area is there. That scene also opens with Vision phasing up from the floor, which I think implies he left whatever room he was previously in.
But really what makes me see it as likely being his room (or his area), is that there’s really no reason for that room to exist as it is. Every other area of the compound, even if we only see it for a second, is not only decorated, its space is also used effectively.
We legit see four sitting areas just in the common room alone. Two tabled areas, two lounge areas (and that doesn’t include the conference room or bar). All of them are decorated, have pillows, lamps, they’re facing each other…
Despite the fact that red lounge area never receives focus for more than a couple of half-second shots, it’s very well decorated. There’s even books on the table, though you can’t see it there.
But Vision’s rest room is such an oddity! The chairs facing a painting instead of each other is basically as meaningful for most people as chairs facing a wall. There’s not even a window to look out of–the only one is so high only someone who can fly could see out of it.
The set designers gave detail to the single second we see of Steve’s office; Wanda’s room was very lovingly decorated; and every other shot of the compound shows they put thought into how it looked. So when they saw the script called for a still shot of a room for Vision to be in stand-by mode in, why’d they choose to decorate it like that?
I could be wrong, but that’s my read anyway.
Those Celestial Bodies 