Ammonia is not dependant upon anything other than ammonia. lol. I take it you understand how the nitrifying cycle works? If not, check out the "Nitrogen Cycle" link in my signature...
Ammonia and nitrIte are bad for your fish, so you really need to keep those levels down as low as possible by doing water changes since you have fish.
It's likely that if the rock you got was really cycled already, that you're just seeing a "mini-cycle" and things might never get out of control.
Continue to test your water parameters, if the ammonia or nitrIte numbers continue to rise consider doing a PWC
In general you want to keep your ammonia and nitrIte levels at 0.0, and your nitrAte as low as you can.