You are right that water conditioners work upon contact. However, you have to think in terms of Prime being like food coloring added to water.In my mind I thought that prime worked instantly and would only treat the water that it got to that instant therefor it would not treat any water added after the prime was added which is why I added it last. Beginner mistake I suppose.
1. Fill 2 cups of water and add 2 drops of red food coloring, and observe. See how far the food coloring goes. Then stir the food coloring very slowly (about 3-4 seconds to complete rotation), and see how it disperses. The longer you stir the more dispersed the red coloring gets at that speed. The faster you stir, the sooner the red coloring gets dispersed.
2. Fill 1/4 cup of water (simulating water in the tank), add 2 drops of food coloring, then add the rest 1 3/4 cups of water very slowly ( like refilling the tank). See how the food coloring disperses and "touches" the new water.
I know that the ratio of food coloring to 2 cups of water maybe higher than Prime dosage and the amount of water you are adding in, but it's just to give you an idea.