The incident started shortly after United Flight 1074 took off around 10:15 p.m. Monday from Dulles International Airport in suburban Washington.
The Boeing 737 jet was supposed to take its 33 passengers and six crew members to Denver, but turned back because the unnamed passenger "failed to comply with crew instructions," United Airlines spokesman Luke Punzenberger said.
Joshua Lindstrom told "Anderson Cooper 360˚" Tuesday night that a man was acting strangely as he moved up the aisle.
"The flight attendant gave some sort of command to stand back, and he turned and started heading toward the cockpit. And the guy in 3E was a lightning bolt and just jumped out of his seat and took the guy down to the ground."
The hero's seatmate piled on and grabbed the out-of-control passenger's legs, Lindstrom said.
Passenger Donna Tellam told CNN's "Erin Burnett OutFront" the men reacted so quickly she thought they were air marshals. She said the unruly man had come down the aisle, screaming about the plane going too slow and flailing his arms.
A flight attendant used plastic ties to bind the man's wrists as the plane headed back, she said.
Earlier, a government official with direct knowledge of the incident told CNN that the detained passenger had run toward the cockpit screaming "jihad, jihad."
Lindstrom told Cooper he didn't hear those words but after the flight was back on the ground the man who tackled the unruly passenger mentioned it.
"He said, 'Did you hear it? Like he said 'jihad' a couple times (while he was being restrained)," Lindstrom said. "... In the end it was more surreal than it was scary. It was wild."
Lindstrom said two other people helped keep the man on the floor for the 20 minutes or so that it took the flight crew to return to Dulles. During that time, the subdued man's mood would change. The man was rattling on about someone trying to bring the plane down, then become despondent and cry, "I'm sorry, I'm sorry."
A cell phone video shows the man, bruised on his face, being held down. At one point, he pleads, "Please stop, please stop, they said call it off." At another, the man seems to cry as he says, "I'm so sorry."
"Don't move," one passenger says, apparently trying to calm the man. "You're OK. We're going to get you off this plane, buddy."
The plane returned to Dulles around 10:40 p.m., said Kimberly Gibbs, a spokeswoman for the Metropolitan Washington Airports Authority, which runs the northern Virginia airport.
Airport police took the unruly passenger off the plane, and airport firefighter-EMTs transported him to a nearby hospital, according to Gibbs.
As of late Tuesday evening, the passenger had not been arrested or charged with a crime, officials said.
There is nothing, so far, in the tackled man's background to suggest he has a connection to terrorists, the government source said. No weapons were found after he was subdued.
By then, the other passengers -- none of whom was injured -- had been rebooked on new Denver-bound flights. Some opted to take the first flight to Colorado on Tuesday, while others chose to leave later, according to Punzenberger, the United spokesman.