Is it right that while my daughter earned <$4k on W-2 got a full refund, my son who earned <$3k on 1099Misc needs to file self-employed and pay $500+ tax with no refund?

Recommended. thanks

That would be correct.  The income received on Form 1099-MISC with an amount shown in box 7 is for self-employment income.  Self employment taxes are assessed on the net profit from the self-employment.
SE taxes are for Social Security and Medicare taxes, both employer and employee share.  The SE taxes are based on 92.35% of the net profit and taxed at 15.3%
Since the income was less than $12,000 there would no be any Federal Income Taxes owed.