Just to clarify one point, it is always legal to pay someone as non-exempt. The reverse is not true.

However, I absolutely agree with Mr. K; your employer needs to pick one or the other and stick with it. He does not get to switch you back and forth either way. Either you are exempt and get paid your full weekly salary every week in which you perform any work at all (limited exceptions apply) but are not entitled to overtime, or you are non-exempt in which you only get paid for the hours that you work, but you get overtime at the rate of one and a half times your regular hourly rate any time you work more than 40 hours in a week.