It doesn’t really matter what your contract says, what matters is what you do and how the company copes with it. And what’s important is whether your wife can get a job elsewhere.
First, the supervisor has no power like that. So the first thing is to ask what she gets paid for being on call - it should never be for free. And if he says “nothing” the next step is to go straight to the next higher up in the company and check whether this is a company policy or whether it is just a stupid idea of her supervisor. (This thing is so unusual, I wouldn’t be surprised if it was a stupid idea of the supervisor, and quite possibly an attempt at bullying).
If it’s company policy, then one possibility is for her to use the phone as normal, and if she gets called to do extra work while she sits at home and is bored she goes to work, and any other times (like sitting at home reading an interesting book) she replies that she’s reading an interesting book and is not coming.