"The first year was hard," he says.
After beginning his studies in finance and accounting, he set about finding work and distributed 102 copies of his CV around Auckland before finding the first of three part-time jobs — including pumping gas at a Shell petrol station — he had while studying. Improving his English, rather than money, was the main motivation for taking on the jobs, Cui says.
He entered the world of banking as an ANZ teller in 2003 and moved to the BNZ in 2005, where he worked in a range of roles before setting up the bank's Asian banking team three years ago.
Cui says his own experience as a migrant help him understand the difficulties his customers face assimilating.
"The people within our [Asian banking] team all come from migrant backgrounds — they've gone through that difficult period until they integrated," he says. "We know how hard it is."
BNZ's Asian banking unit has a range of responsibilities, ranging from facilitating clients' property investments to business banking.
Cui believes Chinese demand for New Zealand property — a controversial issue — is largely a result of soaring property prices in China.
"Property in New Zealand is relatively cheap compared to China," he says. "The costs have gone through the roof so if you sell one apartment over there you can buy a million dollar house [in New Zealand] easily. So why not?"
He says the opportunity to buy freehold property, which is not available in China, is also attractive to Chinese buyers.
Cui believes controversy about Chinese investors contributing to soaring property prices in areas like Auckland is mostly the result of a "misunderstanding between cultures".
BNZ chief economist Tony Alexander said last year that the "sprawling anecdotes regarding Auckland properties being snapped up by Chinese buyers are not supported by the evidence".
But Alexander has also advocated a ban on house sales to non-residents, saying the issue had the potential to cause "societal discord" and threaten New Zealand's trade relationship with China.
While Cui's team facilitates plenty of inward investment from China, it is also looking to expand its business helping New Zealand firms enter the Chinese market.
BNZ is working with Auckland business incubator The Icehouse on the development of a China market entry programme for local businesses.
Cui says the programme will help businesses evaluate whether they are ready for entering China, a notoriously challenging market.
"Hopefully, we'll create a real pathway for Kiwi entrepreneurs."
Cui says the capabilities of BNZ's parent company, National Australia Bank, in Asia are often underestimated when compared with the bigger presence its Australasian competitor ANZ has in that part of the world.
Instead of acquiring stakes in local banks and developing a significant branch network in Asia — like ANZ — NAB has instead focused on supporting the investment and trade requirements of its domestic clients in Asian markets.
Outside banking, Cui is involved in community organisations including his role as vice-president of the NZ Chinese Youth Chamber of Commerce.
So what's his advice for young Asian Kiwis trying to make their way in the world?
"Young Asians born in New Zealand need to make sure they don't lose their traditional Asian culture — there's a lot of history and good things they need to understand such as working hard, [placing importance on] education and supporting family," he says.
"For those new to New Zealand, they need to make sure they get their English sorted before they learn other skills — it's very important."
Frank Cui
• Age: 32
• Born: Daqing, Heilongjiang province, China
• Arrived NZ: January 2001
• Current role: Head of migrant banking, BNZ