Stress Coat is a water conditioner with aloe in it, Stress Zyme is a bacterial additive. basically it puts beneficial bacteria into the water as it conditions it too but no aloe in it.
Stress Coat should be used as a regular water conditioner, so just get water from the tap, and pour in double dose of Stress Coat as per the directions on the back and then pour into the water gently
So no, you don't need to add more to the tank, there would be no point in that unless you didn't pour enough in the first go around.
You say "stored water" are you aging your water? If so, you don't need to if you use water conditioners. That's the beauty in water conditioners, it allows you to pour the water in right away **of course make sure it's the right temp first
a trick if you need to; run the tap and hold a glass thermometer underneath the flow to get the right temp! usually 78-80 is best of course