If you owe no additional tax on the distribution, then the 10% that was withheld from the
distribution will be used to pay the penalty when you file your return
with its 10% penalty.
The "10% penalty" was not assessed at the time of the distribution. It is not
assessed until you file your tax return. And the amount that was
withheld is
credited against the income tax that you owe as a result of new taxable income
from the distribution and the 10% penalty.
After you took the distribution, the check you received was
the difference between the total distribution and the amount of federal
income tax withheld. This is shown on the 1099-R that you received, in
boxes 1 and 4 respectively.
If the withholding in box 4 of the 1099-R was 10% of your distribution, then
it sounds like the plan administrator withheld enough for the penalty but
nothing to cover any additional income tax. The plan administrator would have
no idea of how much tax you would owe when you file, so round numbers like 10%
or 20% for withholding are common.
