A few other factors may be in play here.
On the Auckland Nadi track, the junction between Nadi Oceanic and "Domestic" airspace is at 100 nm from the Nadi DME which is located on a hill just to the NW of the Airport. And if the Air NZ was destined for Nadi then the change from oceanic control happens some distance (20 - 40 miles) outside the 100 nm rep point.
Nadi is a proceedural environment, NO RADAR, so the separation standards are substantially larger than a radar environment that we are in most of the time.
TCAS systems, depending on the make and model of the equipment fitted to your aircraft will pick up and display other "targets" at often a considerable distance. When you get the "Traffic Traffic" warning and a Resolution Advisory it is then that there is a question of whether the separation standards have been maintained.
If the Air NZ 767 was bound for Honolulu via overhead Fiji, then they would have remained with the Oceanic controller removing the two controller/ airspace level of the "Swiss Cheese".