Satan: You read that overblown press kit they call the Bible. You know what you're going to find out? Shit happens.
Satan: Sometimes, Hell comes to you.
Father Kovak: You think you've seen everything? There's a whole world you've never dreamed of. Thomas saw it, and it destroyed him.
Jericho Cane: I've seen a lot, but nothing would ever make me cut out my tongue.
Father Kovak: Wait a few days.
Satan: How do you expect to defeat me when you are but a man, and I am forever?
Bobby Chicago: You'd be amazed what you'll agree to when you're on fire.
Bobby Chicago: You know, sometimes you border on competent.
Jericho Cane: I know, it's scary isn't it?
Bobby Chicago: Is this considered interfering with a police investigation?
Jericho Cane: Hey... we're private citizens having a conversation with another citizen. I mean, I don't think they found a way to outlaw that... at least not yet.
The Man: Something good happens, "It's His will." Something bad happens, "He moves in mysterious ways."
Cardinal: We're not afraid to die for our cause.
Jericho Cane: Good, because I'm not afraid to kill you.
Answer: The Vatican is aware of the birth, somewhere in the world, of Christine (though not knowing her identity at the time), and the Satanists are present at her birth and know that she is "the one." It's safe to assume that the Vatican, and the Catholic Church in general, has spies/informants in the Satanists' society, and were able, in the intervening 20 years between Christine's birth and the events of the film, to track her down to New York and send Aquinas there (the fact that he was sent by the Vatican is established).