When people meet Tramell Tillman, they expect him to be like Seth Milchick, the cheerfully menacing manager he plays on the Apple TV thriller “Severance.”

“After people get to know me, they’ll say, ‘Oh, my God, you’re so nice,’” said Mr. Tillman, 41, who won an Emmy Award for best supporting actor in a drama series last year. “They’re surprised I’m not the scary, authoritative guy we see in ‘Severance.’”

Mr. Tillman got the chance to show off that charisma opposite Tom Cruise in “Mission: Impossible — The Final Reckoning” last year, and he made his Broadway debut in the 2019 production of “The Great Society.” This month, he will star as a character named Bill in “Spider-Man: Brand New Day.”

He recently spent a Tuesday with The New York Times as he shopped for furniture in Hell’s Kitchen and danced through Chelsea.