Your tap water is probably treated with chloramine rather than the more common chlorine. Chloramine is chemically bonded ammonia and chlorine and is much more stable in water and therefore a more affective water treatment product. Unfortunately for fishkeepers (or axolotl keepers) chloramine is an ammonia source in your tap water.
This doesn't mean you cant use your tap water, it just presents a problem.
Most water conditioners will break the chemical bond in the chloramine, releasing chlorine and ammonia. The water conditioner will also remove the chlorine leaving the ammonia, which in a cycled tank, the nitrogen cycle will quickly process out the ammonia. Prime as a water conditioner will also detoxify some ammonia for a day or two.
Im assuming you didnt cycle the tank before getting your axolotl. What do you know about the nitrogen cycle? Do you know how to cycle a tank?
Just to give you some short term comfort, ammonia isnt the danger you might have been led
to believe. Its toxicity is pH and temperature dependant. The higher these are, the more toxic it becomes. At typical aquarium pH and temperatures, ammonia can get quite high before it becomes an immediate problem.
At your 1ppm ammonia and say 18c water temperature, you would need a pH of 8 for it to become an issue.