As Robert Kelly recalls the TV interview that went viral after his children interrupted it with perfect comic timing, he pauses. James has been playing on the floor of his home office but wants some attention. “Hey, Daddy’s on the phone, little buddy,” Kelly tells him. But James won’t hear it – he’s only one and it’s the end of a long day. He gets to sit on his dad’s lap so that his latest interview can continue.

An American academic and expert on Korean relations, Kelly, 45, spoke frequently to the global media from the apartment he shares in Busan with his wife, Jung-a Kim, Marion, four, and James. When the interviews were live, he would lock the door of his study. “This time I forgot,” he says.

Kelly, a political science professor at Pusan National University, had worn a suit and tie to discuss the impeachment of South Korea’s president on BBC World News. As Jung-a Kim tried to film it on the TV in their living room for Kelly’s records, the children slipped her grasp. The couple watched what happened next on their respective screens, along with a global audience that would soon explode across social media.

“I could see the picture on my screen and so immediately saw that Marion had come in behind me,” Kelly says. The girl, dressed in a bright yellow jumper, bounded up to her father’s desk. By the time Jung-a Kim had noticed the incursion on the TV and scrambled to retrieve the children, James had piled into the study on a rolling chair. “I couldn’t understand why the BBC was carrying on with the interview,” Kelly adds. “Maybe they realised right away that this was comedy gold.”

It was, but it wouldn’t be funny for the family for a while. Right after the interview, Kelly joined his wife in the hallway. They were stunned. “We both assumed that was the end of my career as a talking head,” he says. “I thought I’d blown it in front of the whole world.” He opened Twitter, which he used sparingly to promote his work. About an hour after the interview, a BBC News producer asked him for his permission to share the clip. “What would that mean,” the academic replied. “Is this the kinda thing that goes ‘viral’ and gets weird?”

Still not realising how weird things would get, and wary of saying no to a broadcaster he felt he had failed, Kelly agreed to the request. The academic, used only to the kind of notoriety that came with foreign policy op eds in the Wall Street Journal, was about to gain an unwanted diploma in viral fame.

In the coming hours and days, calls and emails poured in from newsrooms and TV studios. Reporters doorstepped his parents in Cleveland, Ohio, as well as his current and former students. The Ellen Show wanted the family on. A lot of the interest fell on Marion, who had stolen the scene with her innocent swagger. As she became a meme in her own right, her kindergarten deployed a security guard. “They were worried some weirdos would show up,” Kelly says.

While the clip was greeted with joy, the inevitable viral backlash loomed. A race row erupted when people assumed Jung-a Kim was a nanny. Then Kelly faced criticism for the way he had attempted – gently – to push Marion away from his desk. “People were reading stuff into our relationship and, oh my God, I didn’t want to get near any of that crap so we didn’t say anything,” he says. “It was a comedy of errors, a family blooper. There was nothing to say.”

The attention became so intense that, five days after the interview, Kelly had been unable to work and was largely confined to his apartment. So his university organised a press conference. The family also returned to the home office to talk to James Menendez, the BBC presenter who had conducted the first interview.

At last the storm began to peter out. Nine months later, the family still gets recognised, and Kelly refers to his brush with fame when he gives talks and attends conferences. The requests for expert analysis soon returned, meanwhile. “For two weeks we were the most famous family on earth,” he says, as James begins to get restless again. “I guess that’s an achievement? I don’t know, it’s still just weird more than anything else. It’s nice to think we made people happy, but it’s not really the kind of thing you’d ask for.”