Sorry you can't have a tax due deducted from the other refund. Not possible. Federal and state are completely separate.
Did you get the state refund yet? It should be for the full amount. At the end Turbo Tax just shows you the net federal and state combined. But that is only for your info. You will still get the full refund and need to pay a tax due.
Check for a state refund
https://ttlc.intuit.com/community/refund-status/help/how-do-i-track-my-state-refund/00/25571
You must have misunderstood something. Taxes owed can
Never
be paid from a tax refund, federal or state.
In the File section on Step 2 of the program you were given several options on how to pay the federal taxes owed, paying from the state tax refund was Not one of those options.
You can pay the federal taxes owed using the IRS payment website for Direct Pay - https://www.irs.gov/payments