They can order it only if they first reported it to you, gave you ample time to correct the problem and you failed to do so. But, if they failed to communicate their concerns to you IN WRITING, they are not entitled to be reimbursed.
Now, do you have a copy of the "report"? I would have that report reviewed by someone else and if verified. CORRECT THE ISSUE.
Have your tenants been complaining about other items? Have they recently lost their jobs, etc? Sad to say, but these are common issues that tenants bring up. "MOLD" is the hot button topic. They like to use it to get out of a lease, out of paying, etc.
If there is mold, you need to get it corrected. But if they didn't raise the concern with you prior then you do not need to "reimburse" them for it. Get the report, have your own person review it.
Offer them the chance to move out and break their lease without penalty. If they really feel there is mold, they should jump at this chance.
Yeah, this is the cynical side of me coming out.