No, you don't need to give us the whole (back)story. But you need to have that mapped out, including how his attitudes change, so that when he does tell us things he's telling us things from a consistent story, and so that you have specific things he can tell us, even if he's vague and cagey.
I'm rewriting (at an agonizing pace) the Erevain episode because having a generic tinfoil hat type didn't work for me. So now Erevain's mentor has tumbled onto some nasty secrets. I haven't got every one of them nailed down, but there are two secrets under the Academy that I have nailed down. One I've hinted at and it links to backstory that I've given. The other I haven't hinted at yet, but one of my reviewers (was it you?) wondered about economies based on gold. No, they're not turning lead into gold. I do hope the reveal will give people skin-and-bones nightmares, but that's at least five books off, and I have to get the first one out of where it's stuck in the mud. I also hope to use the reveal event to trigger avalanches through several books. After I get Erevain out of the mud, get the Book 1 timelines nailed down, rewrite the training sequences ... you get the idea.
So what is Anthony's backstory, external as well as internal? How does he remember it? How does that memory change with his new understanding? How does he describe the process?
FWIW, I think the external part of the backstory you've given is brilliant for the job it has to do. Of course, how Anthony remembers it and how Catherine remembers it will differ, at least in what the events meant to each, just as they did for Catherine and Matthew.
Have you seen Trouble With The Curve? It didn't get great praise from the critics, but it ought to be a classic date movie. Anyhow, at one point Clint Eastwood's character tells his daughter that he wanted her to have more in life than spending it all "sitting in the cheap seats" and she replies, "You call that the cheap seats. To me those were the best years of my life."