I believe it operates on a site-by-site basis since there's settings to tell it to ignore screenshots of certain webpages (at least they're doing that). So one window is blacked out but the other is visible.

Just gotta remember to set up all the sites you want blocked which I expect to be made as complicated as possible and a little nag window on the bottom left every time I visit a blocked site, i.e., "Recall isn't able to take a snapshot of this webpage" with a big "FIX NOW" button.