So it looks as if the state is taking what I owe them from my Federal refund, is this correct?

 No. TurboTax will show your overall refund, which many of us think is misleading because you cannot actually pay your state taxes out of your federal refund. You must make arrangements to pay your state tax separately. 

 Some states allow you to specify a bank account for a direct debit in TurboTax when you file your return. Other states do not allow payments through TurboTax and you have to make your own payments separately on the state tax website. When you file, you can print a copy of your return and it will come with instruction pages telling you what you have to do about your state tax payment.