The singer - one quarter of veteran vocal act Human Nature - had an important purchase to make.
"The very first thing I do when I arrive in Australia is grab a coffee," he told AAP.
"Even airport coffee is way better than anything we get in Vegas."
Allen and his former Sydney schoolmates Phil Burton and brothers Andrew and Mike Tierney have performed together as Human Nature for over 35 years.
For their latest Australian tour, which begins on Saturday and runs until mid-April, the group will be marking 20 years since the release of their career-defining album, Reach Out: The Motown Record.
The album scored Human Nature its first ARIA award and 15 nominations, and was their first record to veer towards soul music after the band spent the 90s and early noughties in a self-described "boy band phase".
The record also catapulted the group into the US market, including a residency on the Las Vegas Strip performing Motown-themed shows.
Despite their experience, Allen said he and his bandmates still got nervous before a big show.
"We thrive on that feeling," he said.
"I think if you weren't nervous, it would mean you're complacent and that's something we never want to be."
Playing in front of a home crowd holds a special feeling for Allen, who has been based in Las Vegas with the band for the past 16 years.
"It's always great to get back and play shows on Aussie soil," he said.
"We do a lot of what we do for the fans, but also our families and friends who have been there with us the whole time."
Fans can expect plenty of hits from the Motown record to feature in the show, alongside other favourites and new single Upside Down - a Diana Ross cover.
Known for their high-energy choreography, Allen said Human Nature would continue as long as band members' knees could hold out.
"None of us are getting any younger," he said of the group, whose oldest member is now in his early 50s.
"But we're still feeling great, energised and really capable of doing what we do."
The group were tight-knit before the band and Allen said friendship is their key to sticking in the industry for nearly 40 years.
"We still have disagreements, but they're never bad enough that we can't get past them and move forward," he said.
"Those things help us make the best decisions we can."
Human Nature's MTWN20 tour begins in Newcastle on Saturday and includes shows in every state.
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