Damon was on the show with LEGO Batman star Will Arnett.
"Ben really took the Batman thing seriously because [his son] thinks he's actually Batman," Damon explained, referring to Affleck's portrayal of the Caped Crusader in Batman v Superman: Dawn of Justice, before sharing a "twist" in the story.
"Sam was convinced the FedEx guy was the Joker because [the company’s] colors — you know green and purple," Damon said. "So, you know, whenever FedEx comes...[Sam goes ] 'Dad, Dad, Joker is here!'"
"Ben literally is on a first-name basis with this guy because he went out the first day like, 'I'll give you 20 bucks if we pretend to fight because my kid thinks you’re the Joker,' Damon added.
To make sure he doesn’t blow his cover, Affleck even uses his Batman voice when addressing the FedEx delivery man, Damon revealed.
Affleck, who has three childcare, Violet, 11, Seraphina, 7, and Sam, with wife Jennifer Garner, dished to ET last month about how fatherhood has made him "see the world differently."
"When you're a young man in your 20s, part of that is making mistakes and learning from them. I just made those in front of everybody, rather than privately," the 44-year-old Oscar winner shared. "There’s stuff I look back on and kind of cringe at but I always tried to treat other people well. My parents imbued that in me and the mistakes I made were mostly just of the embarrassing kind."