I've done space projects with US companies and so am fully marinated in ITAR processes. In answer to your question: No, you can get around ITAR by just being careful about what information is imported and exported to and from the US. If there was a US engineering office and an NZ engineering office and all the engineering effort was evenly distributed among the two, it would be a nightmare as you'd be 'exporting US technology' constantly, but if all the important stuff is being done in NZ and very little know-how has to go back-and forth across the virtual border with the US then it's more manageable (still involves lawyers and experts though). It doesn't matter than the US owns it financially, it's the transfer of knowledge and stuff across the border (virtual and real) that is the hard bit. As this is basically a NZ company which had to do a paperwork fudge in order to accept US investment, ITAR is not such a problem.
I would assume most of their employees in NZ hold NZ citizenship although I'm unsure exactly how NZ handles ITAR.
They have engineers/technicians based in the US as well and I would assume most of those are US Persons (US Citizens or Permanent Residents). In the US you can get ITAR exemptions for non-US Persons but from my understanding it's a more difficult and much more expensive process so it is only done to recruit very high level talent.
I'm at SpaceX, which is a much larger company than Rocket Lab, and I can probably count on two hands the number of non-US Persons working here.
I'm fairly certain that Peter Beck, Rocket Lab's founder and CEO, who is a Kiwi, lives in Socal now.