No one was supposed to know about this. Julia shouldn't have told anyone about this big secret and they both agreed not to talk about this anymore.
So much so, there was a point where Tony believed that Emily was not his own daughter. He was thinking of her as someone else's child and he was there to fill the father's role for her.
It was pretty messed up, but it helped Tony to feel less guilty to Dawn's mother.
"This is not the time for that!" Jason said harshly, probably because he wanted to buy some time for himself to come up with a reasonable excuse. "Your daughter is going into a labor!"
Jason then dragged Tony out of Dawn's bedroom, where Emily had been taken to the nearby room, from the look of it, she was going to have an early labor.