But towards the end of the broadcast "interview", Jay-Jay's voice could be heard.
"You just interviewed a fake Tom Cruise!" Jay-Jay said laughing, before quickly hanging up, along with the impersonator.
It was met with silence from the stunned hosts, and tears from the show's producer Sam Baxter, who could be heard crying on air.
"Oh my goodness, are you kidding me?" Barnett said. "That's so uncool."
"That is truly disappointing. People think that's actually funny, that's not funny. That is probably one of the more disappointing, shameful things.
"I have to say, he was a good impersonator, but such is life."
Media commentator Jim Tucker absolutely believed the stunt was done for publicity. He said popular radio had a long history of pranks "and long may it continue".
Tucker suspected Barnett and Baxter were in on it.
New Zealand's radio-prank history started with Phil Shone who famously brought Auckland to a standstill on April Fools Day 1949, Tucker said. Shone announced a swarm of wasps was about to descend on the city. He persuaded thousands of listeners to place strips of paper smeared with jam or honey outside their homes, close their doors and windows and to don protective clothing before wandering outside. The wasps were a hoax.
Tucker said that as long as the joke is harmless and done by "popular radio" it's fine. If Radio New Zealand started pulling pranks it would be a different situation.
"As long as it's not going to injure anyone it's just good for a laugh.
"If it's a prank that harms the public it's a different ballgame, or if it's done by a media outlet that otherwise behaves responsible and sober it's a bit different."
Barnett released a statement later in the morning hoping Cruise would hear of the controversy and reach out to the deflated Si.
"At the time my overriding emotion was one of genuine embarrassment, I've always wanted to meet this guy. I can now see it was a joke and in the grand scheme of things maybe Tom will feel sorry for me and sit down for that glass of wine," Barnett said.