Right - I have just phoned Auckland Airport for you.
If you are transiting from Auckland to another NZ airport then you DO NOT pay departure tax. She told me that DEPARTURE tax is for when you leave the country and not when you go on a domestic route. The only time you would pay is on your journey back out of NZ. For your journey you do not even need an exemption sticker.
I know we didn't pay it when we came down from Auckland to CHCH in November but wanted to clarify it before posting the wrong information for you.
Hope this helps clear this up
Tanya