If I pay for gym membership with taxed income, and it is reimbursed directly by my insurance as wellness benefit, should my employer withhold taxes on the reimbursement?

I use taxed income to pay $500 for annual gym membership. I submit receipt to my employer, who then submits it to my insurance provider as a wellness benefit. The insurance provider then direct deposits $500 into my bank account, separate from my employers paycheck.

My employer says it will then withhold taxes on the $500 on the following paycheck.

I pay for my insurance through my employer. It seems that, if this is taxable, that it should be reported by the insurance provider at the end of the year rather than taxes taken out of a paycheck that does not contain the $500 by my employer.