Credit reporting in NZ is completely different than in the U.S. In the U.S. no credit history is nearly the same as having a bad one.
In NZ, no news is good news, because the only thing reported in credit reports are enquiries and defaults.
Here you basically build your credit with individual banks, if you have an account with them and they can see a good history of regular income going into the account and you've been at the same job for a while then you should be fine.
They won't be looking at your U.S. credit report, I don't think they're even set up for it as NZ has a completely different system.
When I first moved here it took me a while to understand that the U.S. is only part of the world, other countries don't necessarily do things the same or even subscribe to the same systems as the U.S.