Sure they can start a garnishment without notifying the person. No reason to withold the pay stub, though. I call BS on that, and am inclined to believe this person didn't look into it or even glance at their paystub until it happened a few times and they got curious - finally. A month? Really?
Everybody runs a business. That business is their personal finances. How well would a brick and mortar business do if the owner didn't pay attention to being sure they receive what is owed to them? Yeah. They'd do about as well as this DUmmy.