You do NOT pay state taxes due with your Federal refund. You can pay any TurboTax fees out of your refund, but NOT your state taxes. Pay close attention to the steps in the filing process concerning refunds/payments. It is step 2 under the File tab - the same section you file out refund information. I have included a screenshot below.
Every state has a slightly different process for paying state taxes due. Some will allow you to enter checking information on the return and they will take direct debit it out of your account. But, some require you to go to the states website to make a payment with checking account or credit/debit card. You can also just pay by paper check and TurboTax will ask you if you want this option. You will then get a voucher form to print out and send with your check.
The question about when/will is designed to make sure you indicate you will pay the amount due by the due date in April. Otherwise, interest and penalties may be assessed.