Singer Matt Healy is standing on a hydraulic lift at the back of the arena stage, rubbing his slicked-back, natural-coloured dark hair. Dressed down in athleisure and a V-neck top, he turns his back to the crowd and regards the massive screen behind his band, the 1975, with curiosity.

The visuals on this first night of the band’s latest tour have been pretty impressive thus far. “Modernity has failed us,” runs a line from Love It If We Made It (played later in the set), a stark statement from the band’s persuasive third album, A Brief Inquiry Into Online Relationships. But the 1975 do have some uses for the tech age. There is a lot of very shiny stagecraft deployed in tonight’s gig, bumping them up into the role of arena innovators.

For Sincerity Is Scary, Healy unexpectedly re-enacts the song’s video in a pair of chunky headphones and a rabbit-eared hat. A vast hi-res projection of a New York brownstone behind him, Healy cavorts like Michael Jackson down a sneaky treadmill that runs the width of the front of the stage. The band – drummer and producer George Daniel, bassist and keyboard player Ross MacDonald, guitarist and keyboard player Adam Hann – play on, safely behind a row of lights.

The stage set is full of moving light-boxes and glowing squares – nods to this band’s on-off obsession with rectangles. The quadrilaterals tilt, framing and reframing the action, referencing the original neon shape that appeared on the cover of the band’s 2013 self-titled debut album. (Fans have been known to get tattoos of “the box”.) It is, you reflect, a bit like a Facebook game of “how many rectangles can you see? 92% FAIL this simple test” writ large: there are zillions of them. A Brief Inquiry Into Online Relationships (their third No 1), dwells at length, too, on how those rectangles in our pockets suck us in, distract us and warp our sense of ourselves.

It’s hardly the most original of modern complaints, but the 1975 are credible emissaries from a land of surfaces and mistrust: they nail the ongoing experience of how our feelings are being manipulated by our technology more perceptively – and more tunefully – than most. Radiohead, for one, never had a pop banger as blithe as the 1975’s sweetly nagging TooTimeTooTimeTooTime, which considers infidelity while recalling Justin Bieber and Afro-swing.

And they are unlikely to have deployed dancers. The 1975 have always occupied a grey area between pop and rock – indeed, their creation myth involves shrugging off such delineations and making funky 80s arena guitar tunes, against the advice of the entire music industry. Most of tonight’s show feels more like pop in part because of two dancers, the Jaiy twins – thoughtfully non-sexualised in white overalls – whose dance steps Healy ably mimics.

It’s hard to conjure real cleverness out of large venues, where the tendency is to have people flying about for the sake of it. But this band, armed with such a heavy album, manage to pull off a deft conjuring trick or two.

As Healy gazes up at the back wall during The Ballad of Me and My Brain, a track from their previous record, I Like It When You Sleep, For You Are So Beautiful, Yet So Unaware of It, the backdrop buzzes with TV static. As Healy touches the screen, it warps into dazzling colour.

He then steps up, and into the static. From the side, it looks as though he has vanished. It is a moment that draws a collective gasp from the crowd: it’s not so much that Healy has broken the fourth wall, it’s that the fourth wall has eaten him.

Swiftly, the projections shift and Healy is visible once more, standing on a shelf inside the backdrop for one more audacious reveal. The singer is framed to look as though he is inside an actual iPhone, the word “hello” in an Apple-like font above his head. It’s quite a cool feat: toying with depth perception, then making people take pictures of you with their phones, standing inside a phone.

After this, the rest of the band’s set goes by in a blur of dazzling, hyper-lurid digital visuals, the trajectory slightly downhill. It’s not that the 1975 lack for momentum – they just fail to pull the rug out from under the crowd in quite the same way as before.

Healy, too, is more of an enigmatic presence tonight than he has been previously. It might be a case of first-night concentration, or perhaps, a clearer head than in years gone by. Whatever: he prioritises not falling off the travelator, rather than enacting his previous brand of foppish dissolution, or saying a great deal between songs. You can hardly blame him – the last time he was loose-lipped, he had to issue a clarification of his views on misogyny in rock and hip-hop.

When he came out as a recovering heroin user last summer, the internet did not exactly wilt from the shock. Few artists have gone about their business with as much gusto for rock’n’roll cliche as this 29-year-old.

Tattooed, frequently shirtless, when younger, Healy channelled the brash sensuality of 80s stars like INXS’s Michael Hutchence while simultaneously raising a millennial eyebrow at the absurdity of it all; tonight, he seems more contained, even as he gambols around.

The jaded might wonder if smoking opiates was on some bucket list of poses for Healy. More compassionate observers might ponder the need for unquiet minds to self-medicate. Healy, for his part, has been candid in song and interviews about his insecurities and suicidal thoughts, which populate this album even more audibly than before.

As a result, he has emerged as an articulate personality increasingly in tune with anxious times. Tonight, I Like America & America Likes Me (named after a Joseph Beuys performance art piece where he spent three days in a room with a coyote) marks the height of over-stimulation – our collective overload, and Healy’s personal version. Layered with Auto-Tune, Healy sings about his fear of death while the track hits a kind of auditory and retina-singeing peak, tilting at Xanax-addled trap hip-hop.

Having survived the age of 27 – when Jimi Hendrix, Brian Jones, Janis Joplin, Jim Morrison and Kurt Cobain died – the only rock cliches left for the 1975 to embrace are travelling in different tour buses and making a documentary about their group therapy, as Metallica once did.

Certainly, the album they made around Healy’s stint in rehab in Barbados is a sprawling, genre-hopping mashup that reflects both our era of always-on excess, and Healy’s particular responses to his own internal cacophony. That such harrowing fare can be this refreshing live is a coup.