"No not at all. This is a listing of a New Zealand company on the NZX," Peterson said at an NZX function to mark Harmoney's debut.
He said foreign exempt rules enabled a smoother listing process for the issuer.
"But effectively all the benefits that they would get from a listing here, one way or the other, will still work for them," he said.
"We get to showcase the story. New Zealand investors get to invest easily into the story, so it's a wonderful day for Harmoney."
The dual listing arrangements mean compliance costs are lower, just as it is for those New Zealand stocks that have "foreign exempt" status in Australia, he said.
"It's the same in reverse," Peterson said.
Harmoney chief executive David Stevens said the company made the ASX its primary listing because more comparable stocks are listed there across the Tasman, and the market is that much deeper.
"We wanted to list on both, which we have, to give retailer investors the opportunity in both New Zealand and Australia," he said.
Harmony is based in New Zealand.
"It's a big part of our heritage. Our staff are based here, and we feel that it's the right thing to do."
Harmoney's listing followed its successful A$92.5 million IPO, giving it a market capitalisation of A$353m.
The company said the offer drew strong support across institutional and retail investors. Applications exceeded the IPO offer size.
About A$70m will be used to fund Harmoney's growth as it accelerates originations in Australia and New Zealand and the funding of loans by bank-funded "warehouse" facilities.
Voluntary escrow arrangements are in place for all significant existing shareholders, including founder Neil Roberts and chief executive David Stevens.
The company says Australia represents a substantial opportunity, where the total addressable personal lending market is about A$150 billion.
Harmoney's disappointing debut contrasts other successful fintech listings, such as Laybuy's 45.4 per cent gain on debut earlier this year.