It happens on the second night of the interrogations, at roughly seven minutes into the fifth hour [after seven total hours including the previous night]. Interestingly, Agent Coder doesn’t ask Watts at this point if he’s cheating. He does the opposite.
For several minutes leading up to this moment, both agents reinforce Watts’ ego, telling him what a good man and father he is, and how much everyone likes him. Coder, choosing his moment, then tells Watts there is something they know he is lying about [besides the polygraph].
That’s when Watts says barely audibly at 06:52:
I cheated on her.
It’s a significant moment, and even a breakthrough, not because Watts has told them anything they don’t know, but because it was the first big step in getting him to tell the truth, a big truth, after countless hours of back-to-back lying.
Once the truth of the affair was revealed, and it was important to have him “confess it”, it was easier to lead him towards volunteering more information about his family.