No, I assure you, you are not being charged taxes twice on the same IRA withdrawal.
The amount withheld from your distribution and shown in Box 4 of Form 1099-R is not tax that was "paid" at the time of the withdrawal. It is just like the tax withholding that is taken out of your paycheck. It is an estimate, deposited with the IRS for payment of taxes that will become due when you prepare and file your tax return. The tax that was withheld will be included with any other withholding, from paychecks or other sources, as a credit against the amount due on line 16 of your 2018 Form 1040.
Any tax that is owed on a retirement account distribution is computed and paid only when you file your tax return for the year. There will be ordinary income tax on the amount distributed and a 10% early distribution penalty if you were under age 59 1/2.
When you enter the federal tax withheld amount from your Form 1099-R, TurboTax adds that to any other federal income tax withheld from any of your other sources of income (W-2, 1099-MISC, etc.). That total is used to pay the taxes you owe after you have completed your tax return, with any excess refunded to you, or any shortage shown as an amount due to the IRS with your tax return.
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