“It’s been a while since we played into the sunset,” Tame Impala’s Kevin Parker blithely declared at the midpoint of Tuesday’s concert in Minneapolis. The band was in town for two sold-out shows at a venue behind a local brewery, playing for a total of about 12,000 people. It was warm-up of sorts for Tame Impala’s big headlining spot several hours down the road at Lollapalooza on Friday.

The sunset remark was a subtle flex about Tame Impala’s current status as one of the only young rock bands that can headline a major music festival well past dusk. Back in April, Parker’s group was one of the top acts at Coachella, which happened right after the band debuted two new songs, “Patience” and “Borderline,” on Saturday Night Live.

Five months ago, I wondered whether 2019 will be the year that Tame Impala becomes one of the world’s biggest bands. Milling around Tuesday’s concert made that question seem moot. Selling out two large outdoor shows in the middle of America is feat only a small handful of bands in Tame Impala’s 2010s-era peer group could pull off. (Perhaps The 1975 could do it, too, but it’s hard to think of other examples.) Aside from the occasional graybeard in a Greta Van Fleet t-shirt, the audience was also uncommonly young, no doubt due to Tame Impala’s unique ability to bridge the worlds of throwback psych-rock and modern pop, via collaborations with artists like Travis Scott and Lady Gaga.

Tame Impala no doubt is thriving right now. But the band is also in a state of flux. When I wrote about them in March, I was under the impression that a new album cycle (or even a surprise release) was imminent. The new songs, the high-profile SNL appearance, Coachella — it all seemed to be setting up Tame Impala’s fourth record, their first since 2015. And yet … there appears to be no new LP in sight.

In May, the New York Times published a profile of Parker that focused on his perfectionism and control-freak tendencies, traits that made him the sole creative force in a band that’s essentially a front for a solo artist surrounded by hired guns. As I noted back in March, this narrative has been central to stories about Tame Impala from the beginning of Parker’s career. He has long presented himself as a “loner genius” figure in the mold of Brian Wilson or Syd Barrett (or, to use a more contemporary example, Frank Ocean).

But the Times story seemed suspiciously like a form of damage control intended to excuse the album’s delays. The article’s author, Jon Pareles, wrote that Parker had played him “10 tracks in various stages of completion, most awaiting vocal tracks and lyrics.” He likened the songs to Michael Jackson and Stevie Wonder, which would put the new album in the same ballpark as Currents.

“It’s taken shape in my head,” Parker said of the new, as-yet-untitled LP. “When I start making songs for an album, I don’t know what each one’s role is. But by the time I’m finished, each one has a color, each one has an identity, each one has a purpose.”

The main takeaway from the Times profile is that Parker is continuing to tinker with the record as the band tours the world through the end of summer, including two headlining shows at Manhattan’s Madison Square Garden later this month. In an interview published in July by the website Huck, Parker suggested that the creative space that his success has afforded him has in some ways been a hindrance when it comes to actually finishing off the album.