I've found mention of the 'English for Migrants' courses in various places online. It seems that whatever institution the migrant signs up with has to notify INZ when the person takes the course, since the money paid up front is what funds it, and it's compulsory to do the work within five years of arrival in NZ.
For details, you can talk to the English For Migrants Team at the TEC Sector Help Desk.
http://www.tec.govt.nz/Site-information/Contact-Us/ That website has a FAQ section which may be of interest, too.