In a word, yes, you should get paid for on the job training.
According to the Fair Labor Standards Act (FLSA) that was established in 1938, your employer is responsible for paying you for on job training.
Should your employer fail to pay you for your time during training, and you feel you have a valid complaint, you should contact the U.S. Department of Labor.
On their website, you’ll find contact information as well as how to find your local U.S. Department of Labor Office to visit in person.
If you’re offered a job that doesn’t offer payment for on the job training, you should be wary of accepting the position. In some cases, you may even be asked to pay for your own training.
If you feel uncomfortable, ask questions. Don’t’ feel pressured to accept a position if you’re not comfortable.