No - Not saying to sign contracts or put them through some austere Inquisition. But growing up Novus Ordo is much more than simply "going to the wrong Mass." They still need to have the opportunity to see what the Catholic Church really is, the beliefs, the practices, the true culture. A Protestant convert gets a thorough catechism course and goes through an Abjuration of Heresy before being accepted into the Church. Novus Ordo people need some similar chance to get past the "Well I didn't know that!?" stage. A priest is not supposed to give out Holy Communion willy-nilly. He is actually handing out Our Lord - Incarnate. No small responsibility, that. The Novus Ordo person coming, through God's mercy, to the threshold of Tradition, needs to see what it is to be a real Catholic, and know what he is getting into. By the grace of God he will persevere, as we all hope to.
Yes, I think the priest needs to interview them, at least informally, and in no uncertain terms "recommend" very strongly one book at a time. He needs to tell them they probably have a lot of catching up to do, while being kind, charitable, etc. But he needs to impress upon them, with gentle force, that they have an obligation to get up-to-speed. He needs to follow up with them every month and make sure they're actually following his advice/commands. If they are of good will, they won't mind. They will want to become good Catholics. If they don't care, then the priest is at least off the hook.
God doesn't condemn anyone to Hell for acts of someone else's Free Will. What God WILL judge is "did the priest do his job?"