In Heavy Rain, how do Madison and Jayden ever meet?
There is no path that allows them to meet. Jayden learns Madison's name from clues left behind in Paco's room, but the game never explains how Madison knows about Jayden.
Madison: I know where Shaun Mars is... I've got to call that FBI guy, Jayden... He's the only one I can trust... He'll be able to save him.1 (dials)
Jayden: Norman Jayden?
Madison: My name is Madison Paige. You don't know me—I'm a journalist. We don't have much time, so listen carefully. Ethan Mars is innocent. The killer's name is Scott Shelby. Shaun Mars is at 852 THEODORE ROOSEVELT ROAD. Have you got all that?
Jayden: Hold on, how did you know...
Madison: Please, I'll explain later. Call my newspaper, the American Tribune. They'll tell you who I am. Please hurry, Shaun Mars may still be alive.2
They haven't previously conversed, based on this conversation in "Killer's Place". As Jason said, it's an unexplained plot hole. There is no way to change this, though they can meet if busted at Marble Street (during "The Lizard"). Bear in mind, this doesn't affect the story, explanation, or aforementioned "Killer's Place" dialogue.
Between Madison and Jayden's Blue Lagoon scenes, you can sometimes see Madison exiting in the same cutscene where Jayden is entering,3 but they didn't recognize each other because Jayden wonders why a reporter was at Paco's crime scene in his commentary.4