"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.

India 34630
Great Britain 23686
China 21904
Germany 17660
Philippines 14213
France 12567
United States of America 9522
South Korea 6230
Japan 5577
Fiji 4841