Correct. You should send in a payment by the due date 18 Apr if you anticipate a tax owed. Whenever you file your returns you will indicate that you made a payment with the extensions. When your taxes are calculated on your returns those payments will be accounted for and if you paid to much you will get a refund.
In TurboTax in the "Deductions & Credits" tab in the "Estimates and other taxes paid" section using the "Income Taxes Paid" topic you will enter those state extension payments.
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