You must have misunderstood something. State taxes owed can Never be paid from a federal tax refund.
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,
https://ttlc.intuit.com/community/state-taxes/help/can-i-pay-my-state-taxes-from-my-federal-refund/00/26288
Check the printout or PDF of your return; look for the state cover sheet with the Turbo Tax 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.
https://ttlc.intuit.com/community/refunds/help/what-are-my-options-for-getting-my-state-refund-or-for-paying-any-state-taxes-i-owe/00/25954
I'm glad I saw this because I read it wrong too, although I swear it said "Pay my State tax due from my Federal refund". I mailed a check anyway just in case and sure enough, my Federal refund only had the fees deducted. There was no way to go back and look it up in TurboTax so it's kind of confusing.