I think this “story” started when The Economist did a filler article about it. The Economist article was based on some pretty weak understanding and knowledge of Kiwis and their culture of spending time abroad.
From there the usual YouTube “experts” started stories on it. You know the type - they sound authoritative but they are basically regurgitating stuff from Wikipedia (or some Economist article) with some pretty screens and clickbaity thumbnails.
Ultimately, there’s nothing behind this story. As has been the case since Pakehas arrived, lots of Kiwis go abroad and spend lots of time abroad, some go back, and some don’t, and meanwhile NZ’s population continues to grow.
The trends grow and shrink based on relative health of the Aus and NZ economies.