"If you receive it outside your regular paycheck, then it becomes supplemental and your commission is taxed at a rate of 25%"

As Bill pointed out, and in Pub 15: "Withholding on supplemental wages. P.L. 115-97 lowered the withholding rates on supplemental wages for tax years beginning after 2017 and before 2026. See section 7 for the withholding rates."

There are three ways to compute the withholding, seen in Pub 15.

There are two rates to use, if using the Flat rate, as seen in Pub 15.

22% up to $1m bonus; 37% afterwards. That is Withholding, not Tax Rate. Tax Rate is: this amount contributes to the bottom line of the 1040.

This employer made an error (pretty significant). Your client should have had the usual Payroll taxes, including FUTA, SUTA, SS, Medicare credits, and perhaps even retirement credits/deduction/matching.