It's not possible to pay state taxes out of a Federal refund. See this FAQ:
https://ttlc.intuit.com/community/state-taxes/help/can-i-pay-my-state-taxes-from-my-federal-refund/0...
The Tax Home page in TurboTax is just referring to a summary that shows the net amount you have left when considering both a Federal refund and state taxes due. I admit it can confuse one, and we have complained about that screen and how it adds the Federal and state results together like that. But TurboTax does not automatically pay state taxes due out of a Federal refund. That screen just shows the net effect of the 2 returns.
See your state tax agency's website for methods to pay your state taxes due.