If your drinking water has chloramine disinfection it will contain ammonia. Most saltwater test kits are not accurate on fresh water either.
What you are seeing is the biggest complaint with API test kits and the reason most experienced hobbyists only use them during the initial cycle when exact levels are not critical. Once the tank is cycled it is better to invest in kits like Salifert, Elos or some like Red Sea Pro which I personally don't but all are much more accurate and easier to use since the colors are not shades of the same color but actual changes like from red to blue and very dramatic.
If you are just starting I wouldn't worry much about it, as the ammonia goes down, the nitrites will rise then as the nitrites go down the nitrates will rise and then it is time to start doing normal water changes to export the nitrates. Ammonia is food for the bacteria which and the bypproduct is nitrites which is food for different bacteria which produces nitrates and completes the nitrogen cycle.