Say I shutoff the water at the main of a 2-story house. I open a faucet on the first floor. How long should it take for the water to stop running from that single faucet?

Will ALL the water from the second floor need to be emptied through that faucet before I can begin work on the plumbing? I noticed it takes a minute or two for the faucet to finally stop running. Is this to be expected? I've mostly only worked on 1-story houses where shutting off the main, then opening a fixture will almost stop immediately.