Based on the Program Guidance PDF, you would not be covered for the fall semester (assuming you are starting in the fall). The tuition is covered for any coursework in progress during the supported years. I.e, if you start a semester in May, and the support stops June 30th, it would cover the tuition since it is currently being taken during that year. You would not get tuition support if semester starts mid July.
In my opinion, if you want flexibility, do not go for the third year. 3 months for a whole additional year of service seems not worth it to me.