They might be filling orders manually as some suggested. A Turker working for Zinc.io and placing the orders via their affiliate links would do the trick. No need for negotiations etc.
You can't refer yourself, else the program wouldn't work -- everyone would sign up, everyone would click their own links, and Amazon would effectively have dropped its prices across the board while adding a rebate-processing overhead to every order. That's why program agreements virtually always prohibit this.
