whats the ph and temperature, also do you have an airstone in the tank, depending on the ph and temperature the ammonia could be quite harmless but still be making the water a bit ripe.
at ph 7.4 - 7.6 15°c - 18°c (which are the ideal ph and temp) ammonia at a level of .25ppm is harmless, as the ph and temp goes up so does the toxicity, this is because the test measures TAN (total ammonia nitrogen) NH3 + NH4 (NH3 is toxic free ammonia, NH4 is non-toxic ammonium) at ph 7.6 temp 18°c TAN 0.25ppm NH3 is 0.0033 (very low and quite safe), but as the ph or temperature goes up so does the NH3 in the TAN, for example ph 8 temp 18°c TAN 0.25 NH3 0.0081 (still safe though) or ph 7.6 temp 20°c TAN 0.0038 (still very safe) unless your ph and temp have risen drastically the 0.25ppm ammonia is harmless although the ph and temp would be a bigger problem.
when the ph is low there is less free ammonia and more ammonium and although ammonium is non-toxic it is also harder for bacteria to break down, hence why it shows on a test.
there are five reasons for ammonia to show on a test 1. low ph 2. low temperature 3. overfeeding/waste output 4. inadequately size filter 5. un-cycled tank, at this point in time I would first suggest making sure the ph and the temp is correct. make sure there is plenty of oxygen in the water by having an air stone as this is one of the reasons axies start gulping at the surface for air.
also although ideal ammonia for an axolotl is 0ppm the tolerance level is <2ppm provided the ph and temperature is correct.