There is no option to pay state taxes due using your federal refund, so if that's what you were expecting, you must have misunderstood. Does your state have a payment portal on their website? You should be able to make the state tax payment from there.
For state.....you can not pay the state from a federal refund. 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-paying-any-state-taxes-i-owe
For fees.....
See What if the IRS reduces your refund or delays it.
https://ttlc.intuit.com/questions/2552376-what-if-my-federal-refund-isn-t-enough-to-cover-my-turbotax-fees
Then when the IRS does send your refund they won't take the fees out again. They will send you several emails to pay the fees. If you don't pay they will debit your bank account.