An IRA has nothing to do with your employer, or your payroll.

You are confused how taxes work: your paycheck withholding is not your tax, it is an estimate based ont the information you give your employer (remember form w4?, that was you telling them how much tax you think you owe). If that was incorrect, it is corrected at the end of the year (that’s your tax return, where you are refunded extra tax paid, or pay more if you didn’t pay enough). If you make an IRA contribution, you write it on your tax return to claim it as pre tax.

If you want your employer not to withhold tax on your IRA contribution, you can put that on you w4. Otherwise, you will get back any overpayment at the end of the year. In either case, it is “pre tax.” It’s just a question of when you notice the extra money.