"I paid my Federal and State taxes when I made the withdrawal."
Technically, you did not pay the income taxes on this distribution at that time; instead, what you did is set aside some money to be used eventually as part of your overall tax payments during the year.
The plan administrator can't know how much tax this distribution will cost you at the time of distribution because the administrator doesn't know all your tax information.
Not until you do your tax return after the end of the year will you know how much tax you will owe for the distribution. Then for whatever amount this distribution adds to your tax bill, you have set aside tax money through withholding on the 1099-R to help pay for it. The withholding may be too much or it may have been not enough - you won't know until you are ready to file.
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