You mean the Turbo Tax state fee or a state tax due?
You might be misunderstanding. They aren't paying your state tax due from your federal refund. You can only have the Turbo Tax fees deducted from a federal refund. If you owe the state you have to pay it yourself.
You might have seen the screen at the end that shows you the net of federal and state combined but that is only for your own info.
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.
https://ttlc.intuit.com/questions/1900884-what-are-my-options-for-getting-my-state-refund-or-for-pay...