You misunderstood
Your state tax due cannot
It is not possible to pay your state tax due from your federal refund, nor is it possible to pay a federal tax due from a state refund. The federal and state treasuries are completely separate from each other. You may have seen a TurboTax summary of your federal and state amounts that confused you into thinking one was “paying” the other. It is not. If you have federal tax due you can pay by mailing your payment, having the payment taken out of a designated bank account, or you can pay directly on the IRS website. You must pay your state tax due using the state’s preferred method of receiving payment. For most states that will be by making a payment to the state’s own tax website, or by mailing a check or money order.
The state tax can not be deducted from the federal refund. You can only have the Turbo Tax fees deducted. You will still get the full federal refund minus any fees you had deducted. Turbo Tax just shows you a screen at the end showing the Net amount of federal and state combined. But it is just for your own info. You do still have to pay the state yourself separately. See,
Check the printout or PDF of your return; look for the state cover sheet with the Turbotax logo. If you owed tax, it will show the payment information and how/when you decided to pay. Read the state payment instructions carefully since most states cannot be paid from within the TT system and requires additional steps.