Looks like they are in Auckland and you've linked to the Wellington page. But likely it works in a similar way.

It's also possible you can get a rubbish wheelie bin from a local company. I'm not in Auckland but normally the cost of collection is paid for in when you buy the rubbish bags, so you aren't paying twice if you use a wheelie bin from a private company. They also often let you choose a smaller bin, have fortnightly collection, and other options like that.