It's early Spring '15 and British synth-pop trio Years & Years are in the backstage dressing rooms of Glasgow's King Tut's. Frontman Olly Alexander is suffering from a cold and the mood is waning a bit. Beside the buzzing mini fridge filled with cooling Red Stripes, a mobile rings. It's the band's manager calling to tell them that their single 'King' has entered straight in at Number 1, bumping fellow pop sprite Ellie Goulding off the top spot. It's a moment that would set the band steamrolling into venues across the globe, and throw them headlong into a future where two impassioned Glastonbury sets just feels like the norm.

But for the band's bassist, Mikey Goldsworthy, that night at King Tut's has stuck with him. 'We immediately got that burst of energy and life was good again. Glasgow holds a special place for us,' he explains over the phone, fresh from the festival fields. And Scotland's second city will be more than happy to welcome their return as they perform at this weekend's TRNSMT festival alongside fellow Worthy Farm headliner Stormzy and Welsh alt-rockers Catfish and the Bottlemen.

Completed by synth player Emre Türkmen, Years & Years bagged the coveted BBC Sound of… poll, the same year they scored their number one spot. For Goldsworthy, the whole 12 months felt like a marked step up for the band. 'If you drew a graph, it was like slow ride and then a huge spike,' he says. '2015 was the spike, it changed all our lives really abruptly.'

The band's debut, Communion, followed that summer and received a similarly ecstatic reception. Suddenly, they were thrust into a jam-packed schedule of events and showcases ('We were at a Brit Awards, then we were songwriting in LA and then back over for Latitude'), enough to plump anyone's ego. But, despite their diamante pop bombast, Years & Years are something of a humble bunch who genuinely still seem quite moved by the response to their shimmering synth sounds. 'It's hard to take everything in and assess it. You rock up to the gig and see people and think "Oh, they must be lining up for a new ice cream shop or something." And then you're like "Oh my god, they're lining up for us." I still can't put it into words. It's mad, it's still mad now.'

He's not wrong there. Much like 2015's performance, this year's Glastonbury set hit home for a lot of people as frontman Alexander delivered a powerful address on LGBTQ rights. Even Goldsworthy admits to feeling 'super emosh' during it all. Because that's just one of the admirable things about Years & Years. They've artfully managed to tap right into the commercial zeitgeist, with or without knowing it. A week shy of Pride, and Alexander is rallying that change-making millennial ethos against a rising far-right agenda and championing diversity for all.

The same could be said for last year's sophomore release, Palo Santo, which landed just in time to ride the wave of 90s nostalgia. Spice Girls have made their return to sold-out stadium shows while, in a decidedly dirgier setting, riot grrrl icons Bikini Kill are drumming up their old mosh pits in Brixton. But it certainly wasn't intentional. 'Those vibes have always been there even in Communion,' says Goldsworthy. 'Maybe it was just a bit more prominent in Palo Santo. We never really said "OK, this is going to be a 90s throwback album," we just did what felt right,' He pauses. 'We've got good timing, maybe? We've got world rhythms.'

And just as Glasgow was ready for those sounds to leap from the backstage of King Tut's some four years ago, the world is more than ready for them now.

Years & Years play TRNSMT, Glasgow Green, Fri 12 Jul. Tickets at trnsmtfest.com.