Unless you're on reserve, there's absolutely no expectation that you keep your phone on and be contactable. If they call (they don't block caller ID or anything like that), you can answer or not; up to you. If you don't, they may leave a message asking you to call in, but again, there's no obligation. You can wait until show time to deal with it if you like.

Last time they called me, I had just returned a rental car and was a little early, and scheduling called. I answered, and they asked if I happened to be close to the airport -- another pilot had gotten sick on the road, and they were seeing if I could take his place on a different, slightly earlier flight, and then deadhead home. I said sure, since I was already there. Since moving my showtime earlier triggers 1.5x pay for the day, I made an extra ~$700 to get home an hour later. Win-win.