According to New Zealand Inland Revenue Department, even if you don't bring the money back to New Zealand, you are required to report your income world wide. Below citation and website are for your further reading references.
"Is this how offshore corporations work? If so what can I do with the funds, presumably not bring them to New Zealand?"
I worked for the U.S. tax authority and still personally do forensic accounting. And I have seen many taxpayers with an overseas tax shelter under a business design ended up paying back taxes and penalties of civil and criminal consequences. It is suggested that here that "don't try the overseas tax shelter at home." Even professionals with written tax attorney and CPA opinions can end up later with severe consequences with the government.
As we can observe from the website links below, New Zealand places much emphasis on foreign earned income and global income, business or personal. It is much also an focus of its current political subject as you are aware of. See http://www.nzherald.co.nz/business/news/article.cfm?c_id=3&objectid=11607336
This subject is a global governmental emphasis now. Much emphasis is on the data exchange between countries. It is suggested here that no matter where the income income is earned, the New Zealand taxpayer properly reports worldwide income to New Zealand and follows the tax treaties signed by New Zealand with other countries.
Please continue to refer to the citation and website links below.
Fiona Chen, MPA, Ph.D., CPA, ABV, CFF, CITP
"What overseas income will you be taxed on
If you are a resident of New Zealand for tax purposes, you will be taxed in New Zealand on all of your "worldwide income". This is income derived from New Zealand as well as income derived from all other countries."