I have been an exempt engineer for my whole career. In general, the only benefit to being exempt is a certain amount of flexibility in hours, but most bosses take advantage of that, as yours clearly has been.
Salary non-exempt means they pay you salary for your first 40 hours in a week (plus lunches), and then pay you time and a half for any time over that. That means your time comes right out of your bosses' budget, instead of coming out of your home budget, so your boss is going to be watching your hours very closely. Until you and your boss adjust, get approval every time you anticipate needing to work overtime, preferably by email or text or some written documentation.