Test your tap water untreated, then test the tap water treated with the same ratio of prime you use to treat your tank. The chlorine and chloramine which are CL2 and NH2Cl, are removed by reactions with two chemicals in prime. The chloramine is stripped of the chlorine to create ammonia. The chlorine in the tap water is also converted to ammonia. The second compound in the prime binds with ammonia to create ammonium which is less toxic to fish but still consumable by your beneficial bacteria.
Unfortunately, the reagent in API test kits will give a false positive for ammonia but is actually showing ammonium which is normally present when you do a water change because of the process outlined above. If you are testing your water after or anytime near a water change this is probably the false positive you are seeing. It probably indicates that you have alot of chlorine or chloramines (I have TONS) which will linger for a while as ammonium until the BB can process it. Seachem claims that the process can't be reversed but I don't agree that the ammonium cant convert back to ammonia at least in small quantities.