"The UK is the largest source of work visa migrants, while China and India account for only a small proportion."
Not true. India is the largest source, by work visas approved, for calendar year 2016. From data on the Statistics NZ website (the same that Andrew Little got his notorious labourer stat), the totals are below for work visas approved in calendar year 2016...
The NZ herald describes "arrivals". I am guessing their figures entirely exclude people transitioning off another kind of visa, e.g., someone who entered NZ on a student visa and transitioned to a work visa. So they are right in saying that the top 5 "arrivals" on work visas are "not Asian" countries, but as you see below, India, China, and Philippines are all in the top 5 total work visas approved.
Great Britain 23686
United States of America 9522
South Korea 6230