At the time McEvoy was a musician for hire. As well being a singer, songwriter and guitarist in her own right, she did session work, played violin with the RTE National Symphony Orchestra and was keyboard player with Irish singer Mary Black's band.
Black had come along to hear McEvoy that night and afterwards she and her husband came up and said how much they'd liked the song McEvoy had slipped in as a set-filler, Only A Woman's Heart. Black's record company was planning a compilation of Irish women singers and musicians to showcase their talents, so how would McEvoy feel about her song being included.
"I said 'sure' but I didn't think too much about it," says McEvoy. "It was one of these songs that I'd written for myself. I didn't realise at the time but I must have been feeling sorry myself so I'd written this lyric that came from the heart but certainly wasn't designed to be a hit. You know, how to be a success: alienate half the population. It also had no rhymes and there are only about four songs in the history of pop music that have become hits with no rhymes. But it obviously caught on."
It did indeed. The projected album, which featured McEvoy alongside Mary Black and her sister Frances, Dolores Keane, accordionist Sharon Shannon, and the now Nashville-based Maura O'Connell, took its name from McEvoy's song and promptly took off, far exceeding Dara Records' projected sales of 3000 copies. McEvoy, however, was unaware of just how popular her song had become after it was released as the lead single from the album.
"A couple of days before the album came out I was signed to Geffen Records by the guy who had signed Guns N' Roses and Motley Crue," she says. "This was a pretty big move for me, and I was away in the States recording and touring. I'd get these messages from home saying, 'You're song's on the radio all the time' and I'd think, what does all the time mean, a couple of times a week? I was too busy and too far away to really appreciate the effect it was having. But then I arrived back in Dublin Airport and it was playing over the sound system. Then I got in a taxi and it was playing in the taxi, and when I got home I switched on the radio and there it was again. And I thought, yeah, this really is being played on the radio all the time."
The album, A Woman's Heart, went on to become the biggest-selling home-grown Irish album of all time, but while her song opened doors and brought in royalties, the income it generated wasn't on the level that would allow someone to retire and McEvoy remains a working musician. She spends more time on the road than she does at home and juggles motherhood with her touring commitments, "praying that the ball I drop isn't my daughter", as she puts it.
Not that she's complaining. She's seen parts of the world she never dreamed of visiting and her daughter, now 11, has accompanied her whenever touring and school holidays can be synchronised.
Back in 1992 McEvoy thought the fuss about the parent album and Only A Woman's Heart itself would last about six months. But the interest continued. A television documentary examined the phenomenon that she'd inadvertently helped to create and when the 20th anniversary of the album's release came round in 2012 she was pleasantly surprised to find that the celebratory concert, at the Olympia in Dublin, had sold out and then gobsmacked when the promoter told her that another two nights and then another two - eventually leading to 12 in all - had done likewise.
"It's amazing to think that, for me, it all came from a song I never meant other people to hear," she says. "But it's obviously affected people and that's a great thing for a writer.
"The anniversary shows were brilliant. There would be panics in case somebody didn't get out of rehab in time and all sorts of stuff, but somehow the show would go on, and the music would be really good.
"For Glasgow we have Sharon Shannon, who's just brilliant, and Mary Coughlan, who's a formidable character, a real force of nature, and myself as the old guard plus Hermione Hennessy, who carries on her dad Christie's legacy, and Emily Smith, a Scottish singer I'm just getting to know but who has a lovely voice. So we're looking back but also carrying the idea forward with a new generation."
A Woman's Heart is at Glasgow Royal Concert Hall tonight.