do spidermites live only on the plants, or do they live and nest threw out the room?

I just moved plants from a friends addic into a newly renovated room for growing purpaces. Since I found spidermites on one of the plants I am whiping down the whole room with insectasidal soap as well as the plants. I plan on repeating this untill the mites are gone.

Should I just remove the plant before the room becomes inffested?
or should it be fine in the room as long as I keep applying the soap?
The plants have been there for a couple of days, is the room already infessted?

__________________
cannabis was put on this planet to be smoked.