Thinking this was just a coincidence, Tappin slipped into one of Flack's hits, Feel Like Making Love, as a joke during his saxophone solo.
After he was finished the woman summoned him to her table and asked him what he was doing in Barbados. Tappin said: "Working. I'm from here."
His inquisitor replied, "No, you need to be with us in New York. I'll send you the tickets" - and that's how Tappin got the saxophonist's job in Roberta Flack's band. Two weeks later he was recording a DVD in Washington DC with the great soul, R&B and jazz singer with nothing so much as a rehearsal beforehand.
Tappin has a fund of such stories, including the times he met and played for Bill Clinton, Barack Obama and Fidel Castro, and will doubtless share some with his audiences when he begins a 10-night Edinburgh Fringe run this weekend. He's met his heroes, including percussionist Ralph MacDonald, who played on the first album Tappin ever bought, Grover Washington's Winelight, and told Tappin his wife thought he sounded just like Washington, then hired him for his band. He's had a limo sent to take him to Radio City Music Hall in New York for his first gig with soul heart-throb Luther Vandross, and he's played with Caribbean music legends from jazz pianist Monty Alexander to reggae star Maxi Priest.
Not bad for the school pupil who had, he says, the misfortune of being able to sing the note that the music teacher played on the piano.
"If you could do that, you were corralled into the choir and given violin lessons," he says. "I thought, I'm getting out of this, so I joined the cadets instead and they said, 'If you can play music, you can play clarinet in the band', and I was stuck with that until I was 15 and got my first saxophone."
It was around this time that Tappin realised that the records his photographer father had brought back from his time spent working in the UK must have seeped into his consciousness by osmosis.
"My dad was a big Sinatra fan and I didn't mind that, but he came back from London with all these Stan Getz, Cannonball Adderley, Duke Ellington and Miles Davis albums that he'd play every weekend, and I did not like that," says Tappin.
"But suddenly I began to hear something I could relate to in them. I started playing gigs with these older guys and eventually I won a scholarship to Berklee when I was 19."
His time in Boston at the famous music school was a culture shock in good ways and bad. He'd hear students three years his junior who were so good that he'd wonder why they were even bothering to study. This made him work - he'd practise from six until midnight after classes - and the knowledge he gained about jazz harmony allowed him to add solid theory to his ability to play Charlie Parker and Grover Washington licks by instinct.
After he'd been stopped three times by the police for no other reason than the colour of his skin, however, Tappin decided to take his qualifications and head home.
"Growing up in Barbados I never even considered if someone was black, brown or white," he says. "They were just people. One time in Boston I got lost and asked these two very respectable-looking women for directions - and they turned and ran like they'd seen the devil. That was funny but other times, if I hadn't been carrying my Barbados passport, I'd have been in real trouble."
Back home things lightened up and he tells another story about acquiring a manager who had seen this saxophonist playing in a reggae band and another one playing in a jazz band - and hadn't realised they were the same saxophonist wearing different clothes.
"He said, 'You should make an album that's jazz and reggae'. So I did and that's how I ended up working with Monty Alexander because he flavours his jazz with the Caribbean."
Tappin subsequently lived in Brooklyn for 10 years, but he prefers the Caribbean pace of life and if Roberta Flack, with whom he still works, needs him, then he can fly off around the world with her from Barbados.
"The Caribbean's in my music," he says. "When I get to Edinburgh I'll read the room to feel what people like. I might play anything from 1934 to 2014, maybe play some bebop and flavour it with calypso or play bossa nova or a blues with a reggae inflection. It's all one to me."
Arturo Tappin: The Horn of Plenty plays the Outhouse, Edinburgh ,from Friday, August 15 to Sunday, August 24