Correlation and causation are very different things. Correlation in the past doesn't mean anything for the future.
With the NZ50G index being compounded dividend reinvestment (the only one I'm aware of in the world) it certainly won't follow the S&P500 unless by chance for a while.
Even if the indexes were compiled the same, I'd find it hard to imagine that one of the smallest markets in the world (all of the NZX companies combined are worth less than a lot of S&P500 companies alone) in a remote export commodity country that flirts with communisim and has an uneducated population, would have the ability to correlate with the powerhouse of the top 500 American companies.
That over certain time periods over the last cycle it has done is a fact but we must think rationally about why and what it means.