It sounds like you are referring to your "Net Refund" Summary Page in TurboTax  TurboTax shows you a "Combined Total" of your Federal and State Returns, but they are not actually combined when you file

Per the details in your question above, you will need to pay the IRS $470 and you will receive a refund from your State, of $222.  

The "Net Balance Due" shown on your Summary page is the combination of these two amounts: $470 Federal Balance due less your $222 State Refund = Net Balance Due of $222.