fish create ammonia --- bacteria consumes ammonia and creates nitrIte --- bacteria consumes nitrIte and creates nitrAte --- water changes remove nitrAte. If you take the fish out of the tank before the cycle has completed (about 4-6 weeks with fish, in my experience) you take out the source of ammonia, so the bacteria that's been building up dies off.
This would definately account for you have no ammonia, [possibly] no nitrIte, and some nitrAte, because the only way to get the nitrAte out of the tank is to do a water change. Unfortunately, it's very likely that your tank is not cycled and that as soon as you put fish in it, the cycle will begin again, which would be very bad for your puffers.