Nah, that's not how it works. Caller ID is surprisingly insecure. Basically, the phone number of the calling party is sent along with the phone call. All you need is special software in your call centre, and anyone you call will see whatever number you type in. So they set up software to automatically generate a phone number that appears to have a similar location to the one they are calling. They call you, it looks like it comes from NZ (or often Australia), but actually they are sitting in a call centre in pretty much any country in the world.

If someone is calling from overseas, there's very little that anyone in NZ can do. Call blocking only works on the caller ID; since you can generate infinite new phone numbers to send along the caller ID channel without needing to actually use that phone, it doesn't do a lot.