An extension is an extension of time to file your tax return, not an extension of time to pay the tax that you owe. The payment due date of April 15 is correct. The penalty for late payment is based on the date of payment, not the date of filing.
After the IRS processes your tax return they will probably notice the double payment and send you a refund without your having to do anything. So just wait a couple of months and see if you get the refund.
