"You know when the guys in Customs start going, 'Saw you on the Letterman show,' and you're going, 'Wow, the Customs Guy!'" she told CBS News correspondent Anthony Mason.
Her debut album, "Eye to the Telescope," sold more than 1 million copies in the U.S. alone and produced a second smash single, "Suddenly I See," which proved that the Scottish singer was no one-hit wonder.
Now she is trying to recapture that magic with her sophomore album, "Drastic Fantastic," which is out this week.
Rolling Stone says "Drastic Fantastic" is "crafted with intelligent attention to every detail." But not long ago, Tunstall couldn't get a record deal.
"They said you're too old," she said. "I was 27 ... And I mean, I'm 31 now, so I looked younger then than I do now. And I was just going, 'I'm not totally haggard yet.'"
A British label finally took a chance on her. But her big break came when a BBC TV music show called and asked her to fill in for a rapper who'd cancelled. She suddenly found herself on the same bill as Jackson Browne, Anita Baker and The Cure. Tunstall stole the show.
Everything's gone right for her ever since. But even during the ten years she was living on the dole and playing coffee shops to get by, Tunstall never lost faith.
As an infant, Kate Tunstall was adopted by Scottish parents, who told her early on that her biological father was Irish and her birth mother half-Chinese.
"Even though I didn't look particularly weird, I didn't look like anyone I knew," she said. "I didn't look like my parents. I didn't look like my brothers. So, it gives you this sort of strange, I don't know, passport to sort of not have to follow any rules."
She was raised in St. Andrews along the stunning eastern coast of Scotland. She showed Mason around her old stomping grounds.
"And this tower, St. Rules it's called, when we were kids we used to go up that because it wobbles in the wind. So if it was windy you'd be like: 'I'm going up the square tower."
She said it was wonderful to grow up there, but she left in her 20s to pursue a music career. But she's remembered by old friends and new fans. She and Mason visited her old place of employment, an ice cream shop where she got a job scooping ice cream at 15. Her old boss, Tony Fusaro, still owns the sweet shop.
"She was great," he said. "And whatever success she has, she more than deserved it."
After her ice cream gig, she graduated to sales assistant at a liquor store where she developed an enduring affection for single malt scotch.
"Such a snob, it's probably my only major diva moment, just going, 'This is blended, take it back!'" she said.
Her father, David Tunstall, a retired physicist and her mother, Rosemary, a retired teacher, admit they worried about their daughter in the ten long years she was trying to make it. They wanted her to get a "proper job." But no one is more proud of her now.
"She went to drama classes. She went to tap dancing classes. She played the flute, played the piano. And I see it all on stage, you know," Rosemary Tunstall said.
This summer, Tunstall's worldwide tour took her back to the Scottish highlands to play an outdoor festival on her 32nd birthday. It was the first festival that she's headlined.
"It's funny doing all that press and they're just saying 'You're not upset you're working on your birthday?'" she said. "And I was like 'Who told you this was work?'"
For KT Tunstall the real gift is just performing. And to all the record labels that said she'd already had too many birthdays, that she was too old to succeed: Too bad, they've missed the party.
"And I had a really, really good birthday," she said to her audience.