I don't mind being contacted on days off because I get paid extra for working on them. Did four a couple of months ago and smiled when I saw my payslip.
Generally we would not be called during a rest period, an SMS would be sent instead. One arrived recently while I was asleep advising me of a change to my roster involving a one hour later sign on. It saved me from sitting around at the airport.
My phone goes on silent while I'm in my legal minimum rest as I can't be called in early. When I wake up I check my messages and turn it back to normal volume.