The residency test for college students is a little tricky. When you are away at college, even if living off campus ("rented my own apartment and paid most living expenses"), for tax purposes, you are considered as still living with your parents and only being temporarily away from their home.
In your case, you do not meet the residency test because you did not return home after the May graduation. So, you did not reside with them from May to December and cannot be their Qualifying Child dependent.
