You can either elect to use the AROTC scholarship for tuition or room and board. There is an election form that gets filled out and it's for the calendar year.
For room and board, the payment is capped at $10,000 per year. If its $10,001 then you are responsible for $1.00. The R&B is more of a reimbursement and in the fall semester is can be December prior to getting paid.
The Cadet gives their ROTC HR person proof of dorm fees and payment and payment of a meal plan. If no meal plan is chosen, then it's a calculation of basically midway between the most expensive and the least expensive meal plan.
If the Cadet lives off campus, they have a way to calculate what the typical rent would be. If you spend more than that you are on your own. You don't just get handed $5,000 per semester unless that is whatbthe determine is normal for the area.
I can tell you that my son gets less than the $10,000 this year even though his apartment off campus is more than his dorm was last year. He ends up with a tad less than $9,000.