No that can never happen. Federal and state are completely separate. You can't pay one from the other. At the end Turbo Tax shows you a summary of the net combined federal and state. But that is only for your info. You will still get the full amount and need to pay any tax due separately yourself.
And Turbo Tax will always show the tax due or refund. It doesn't know if or when you pay or get a refund. That's just the result of your tax return.
If you are looking at the TurboTax Tax Home web page showing your Tax Refund, that shows your Net between the tax refund and taxes owed. It does NOT mean your taxes owed are being paid from the tax refund.
If you recently filed your federal tax return and paid the taxes owed by direct debit from your bank account, it will take a few days before the IRS actually debits your account. There was a high volume of tax returns being filed on the last days on and before the July 15 due date. Because of the pandemic the IRS has fewer personnel handling tax returns.