Can an employer ask an employee to do something that doesn't meet their job criteria without proper training?

Unfortunately, you didn't give us enough information for a specific answer. The short answer is yes. In North Carolina, an at will work state, the employer can pretty much ask you to do anything. The only real limitation would if safety or licensure is a concern. Example: the employer cannot have an unlicensed staff member work a forklift. But if safety is not an issue the employer is not limited by your job description.