The NZ site will be different depending on what country it thinks your IP address is in.

You need to choose the New Zealand version of the site to see the discounted tickets - go to the top right hand corner of the site and it'll say United States or United Kingdom or whatever, click on 'Change' under there.

You could also go to a site like expedia.co.nz which as well as the NZ-discounted fares also features cheaper lead-in fares on a competitor domestic airline.