You need to ask your department. I'm international, and my offer letter (from a state school) explicitly stated that all the tuition, including the non-residential supplemental tuition fee, would be covered. For Americans, I believe it is usually understood that you will establish residency in the new state by your second year, so often the out of state part is only covered for the first year (and the in-state part is covered for all years). But again, you need to ask the department to know for sure. My guess is that it is all covered, though.