Hiya!
I think it's unlikely an aquarium-safe chiller would have interrupted your cycle. In theory, I guess it could be possible for a sudden temperature drop to mess with your cycle, but such a sudden temperature drop would not be safe for any aquarium creature either, so I assume the chiller would not be that extreme.
Small ammonia fluctuations can still happen in a cycled tank. The tank being cycled just means you have a solid population of nitrifying bacteria, that eat the usual production of ammonia. If the tank suddenly produces more ammonia than normal (because left-over food has gone unnoticed, because a plant has dropped some leaves, heck, even because your axolotl took an unusually large poop), you will still measure a small ammonia spike.
The increasing temperature (from before you installed the chiller) could have played a role as well, since higher temperatures means ammonia forms more quickly.
In general, your bacteria population will adapt to small ammonia spikes rather quickly (probably followed by an even smaller nitrite spike). How much ammonia did you measure?
If it's more than a little spike (but a big spike instead!) you might want to search for the cause and do a water change.