In my company you do not have to answer your phone on a rest day, a blank day, or an un-rostered day. You only have to answer your phone on a standby. A rest day to us means the day after a night flight, when you should be resting for either another night flight that night or for your days off. So crewing would never call you on a rest day unless it was to advise of a delay, and even then you don't have to answer your phone.