If it is indeed chloramine, then the API water conditioner will simply break the chlorine-ammonia bond; technically, the chloramine no longer exists (as I believe the API water conditioner advertises that it can "remove chloramine"), but there is still ammonia.
The ammonia will register on your test kit.
If you use Prime, the ammonia will be detoxified (supposedly, locked so that it cannot harm livestock). I am unsure if it still shows up on test kits.
As for your water supply, it is likely not ammonia that is in the water, but chloramines, as you mentioned. This is what the ammonia test kit is probably detecting.