"Their employer is saying the Tax Pro needs to apply for the exemption but I thought the employer is supposed to select the correct code to reflect it was a hardship withdrawal."

Hardship withdrawal has nothing to do with the tax rules. It has to do with the Employer plan provision. It might allow hardship withdrawal, or not. They don't control if it is taxable and/or subject to penalty. This simply is a permitted or not, consideration.

The issuer of the 1099-R usually has no idea what happened to the funds, or if they were even used as intended. The 1099-R is for money Out.

The Tax Pro does due diligence to fill in the tax form filings that reflect what happened.

You didn't mention the specific plan or account type. The IRS has a useful table, here:

https://www.irs.gov/retirement-plans/plan-participant-employee/retirement-topics-exceptions-to-tax-o...

That is specific to the penalty.