The main question might be why you are having to deal with ammonia at all. If this is a tank which is stable and fully cycled, there should only be a bit of ammonia reading as you are doing the water change and nothing to worry about as the bacteria will deal with it as needed. Something is not right with the testing on timing or something. A normal tank, running as it should, should not be showing ammonia as the bacteria will have just grown a larger colony to meet the larger amount of ammonia available.
When we do a fishless cycle, we pour ammonia straight into the tank and wait for the bacteria to grow large enough to deal with straight ammonia poured in. The small amount that comes in through the tap will be no problem for a colony to deal if they are not being killed in some way.
Is there a possible misreading of the colors on the test? Sometimes when we look really hard for a problem we see things that mess with our minds.