"Whenever I get on the field or step in the locker room, I think it's pretty easy to take outside life, leave it at the doors and pick it up as you walk out," O'Sullivan said after his start.
Sabrina went into labor on Tuesday, so the Padres placed O'Sullivan on paternity leave.
"There's probably a part of him where it was probably sort of cool, knowing that he was pitching the day before his son was going to be born," Black said.
Paternity leave allows a player to miss no more than three games. To replace him on the roster, the Padres have recalled reliever Miles Mikolas. In 44 games at Tucson this year, he is 3-1 with 21 saves and a 2.86 ERA.
His time in the Majors this season has been a bit unusual. Mikolas is making his fourth stint with the Padres this season, but he's only made one appearance.
Mikolas pitched a scoreless ninth inning against the Giants on July 11 before being optioned back to Triple-A the following day, then was recalled on July 21, but didn't make an appearance before being optioned back down the next day. The first time Mikolas was recalled was on June 23, but he did not make an appearance.
"Just like any relief pitcher, there's times where maybe you don't throw for three or four days and then maybe you're throwing three or four times in five days," Mikolas said. "So I've been throwing a lot [at Tucson] so it doesn't really mess up a rhythm as a reliever too much, because you're always on call."
Corey Brock is a reporter for MLB.com. Keep track of @FollowThePadres on Twitter. Jamal Collier is an associate for MLB.com. This story was not subject to the approval of Major League Baseball or its clubs.