Welcome to the forum!! You shouldn't have issues with aged water going bad unless there's contaminants in the air. Being in a closet shouldn't be an issue. Using Prime at the time of the water change is the correct thing to do. I add it to the tank and not the barrel.
How many are you getting? If you're new to discus, I would suggest planning on more water changes than once per week at least until you get comfortable with them and how well they're doing with your setup...