In the first case, Tom actually said something like "I will phone you on Sunday". In the second case, he must have said something like "I will have phoned you on Sunday" (which I think would sound better if it were worded "I will have phoned you by Sunday"). Presumably, that means that come Sunday you should have already heard from Tom.
Thanks for your reply. I understand what you're saying but not sure my student would understand this explanation... I'm wondering if ANYONE ELSE here could perhaps explain it more simply or in another way so that it would make it easier for my student to understand?
Tom said he'd phone me = Tom told you he was going to phone you. Maybe he did, maybe he didn't, but he intended to.
Tom said that he would have phoned you = Tom didn't intend to phone you and didn't phone you, but says that if things had been different, he would have phoned you. Imagine he has learned something important that you should know about. He didn't know it at the time, so he didn't ring, but he later told you that his not ringing was because of not knowing the information and not through a failing of his.