The exclusion for a first home purchase only applies to IRAs. The 20% withholding is standard for an early distribution. There is no way to withhold the exact amount of tax you will owe on the distribution since the administrators have no idea what your tax bracket is. Since 10% is going towards the penalty, that leaves you with 10% to actually cover your federal tax. If you are not in the 10% bracket, you can owe.
https://www.irs.gov/retirement-plans/plan-participant-employee/retirement-topics-tax-on-early-distri...
