I agree with abc, but since you did post this in an income tax forum . . .

I've studied the "new" (and improved?) W-4 in detail.  With $54K of income the W-4 "math" will deduct a standard deduction of $12,550 and assume the rest is taxable income.  So let's call that $42K of TI.  Tax on Single w/$42K of TI is roughly $5K BUT adding the 2 kids in Step 3 gets you $4K in CTC, leaving you with only $1K of fed w/h.  If there are fluctuating paychecks (i.e. hourly pay) I could see $1K getting whittled down to your "just over $500" w/h for the year.

So this might not be wrong even though it's not the desired outcome.

With 2 kids, does that put him into HOH filing status?  That may make a difference but I'll assume not since you didn't mention it.  Their ages will make a difference, and the amount of advance CTC plugs into the equation as well.  The "2021" problem is that your client already "collected" $2,000 per kid of the child tax credit via reduced withholding (thanks Step 3!) and then was likely also paid $1,500 - $1,800 per kid directly from the IRS (thanks ARPA!)  If the credit allowed is only $3,000 per kid (i.e. they're both 6+) but he already collected $3,500 each then he has to pay part of that back.  Welcome to unintended consequences.

Without knowing pay frequency and number of pay periods so far this year I can't really speak to the $10.67 on $5,840 but it's not necessarily out of the ballpark either, especially if we're talking about 4 pay periods YTD.

If he needs more withheld, either drop one or both kids from the W-4 or use Step 4 for either other income or extra withholding.

Rick