The drivers of the price of New Zealand emission units (NZUs) in the market are supply and demand. Most trading of NZUs happens in the secondary market, instead of with the Crown. See Where to buy emissions units.
The price controls only operate at auctions and do not prevent secondary market prices from going above or below these prices.
The Government has also implemented a confidential reserve price, which prevents NZUs from being sold at auction at a price significantly below the secondary market price. If the auction clearing price is less than the confidential reserve price, no NZUs will be sold at the the auction. Unsold NZUs will be rolled forward to be sold at the next auction if it is in the same calendar year.
To learn more about the purpose of price controls, and how they relate to emissions budgets see the role of price controls in the NZ ETS.