If you are looking at the Tax Home web page where it shows your total refund, that is NOT an indication that the state taxes owed will be subtracted from the federal tax refund. That is only the NET you will receive between the refund and the taxes owed.
You will receive the full amount of the federal tax refund. You will have to pay the state taxes owed based on how you chose to pay those taxes in the File section of the program before the tax returns were filed.
The state tax can not be deducted from the federal refund. NEVER. 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.
Your only proof of payment is your bank statement or credit card showing the payment coming out. Turbo Tax only passes your bank account number to the state for the state to take it out of your account. But most states do not let you pay by Direct Debit so you have to mail in a check or go directly to the state's website to pay.