Maybe the responses about "Time to find a new employee" are jokes, maybe not. But just so you know, if DOL were to perform an investigation and conclude that you fired the employee because he made a complaint about failing to follow the wage rules, that can get you into a seperate extra amount of trouble.

Federal labor law is explicit about who is exempt from receiving overtime pay: Educate Yourself

"There are two ways in which an employee can be covered by the law: "enterprise coverage" and "individual coverage."
Enterprise Coverage
Employees who work for certain businesses or organizations (or "enterprises") are covered by the FLSA. These enterprises, which must have at least two employees, are:
(1) those that have an annual dollar volume of sales or business done of at least $500,000
(2) hospitals, businesses providing medical or nursing care for residents, schools and preschools, and government agencies
Individual Coverage
Even when there is no enterprise coverage, employees are protected by the FLSA if their work regularly involves them in commerce between States ("interstate commerce"). The FLSA covers individual workers who are "engaged in commerce or in the production of goods for commerce."
Examples of employees who are involved in interstate commerce include those who: produce goods (such as a worker assembling components in a factory or a secretary typing letters in an office) that will be sent out of state, regularly make telephone calls to persons located in other States, handle records of interstate transactions, travel to other States on their jobs, and do janitorial work in buildings where goods are produced for shipment outside the State."

"When an employee earns a salary, he or she is paid the same amount of money every week, regardless of how many hours that employee worked. While many people, including many employers, believe this makes these employees exempt from receiving overtime pay, an employee must fit into one of three categories in order to be exempt from overtime. If an employee can be classified as an executive, a professional, or an administrator, then that employee is likely exempt from overtime pay. There are very detailed laws regulating the job duties that make an employee exempt from overtime."