Trustee making distributions from an Inherited IRA to beneficiaries

I disclaimed my inherited IRA which is owned by a trust so that it would pass to my children. My husband is the trustee and my 4 children are the beneficiaries. We knew that the trust would produce K-1s for the distribution to each child and each child would pay the tax (at their lower rate).  We were thinking we were wise in withholding the State and Fed taxes that each child would own based upone their tax bracket. However, those withholdings were made during the distribution from the trust that holds the inherited IRA. ...I don't know, but I think we goofed. If the withholding were made during the distribution, would that mean the trust paid taxes on the full distributions?