are you using test strips or another form of testing? in my experience the strips can show mild to moderate inconsistencies. also check your tap waters nitrAte level, as some districts have 5-25 straight out of the tap, so sometimes lowering nitrates to 0 must be done with plants or anaerobic bacteria.
as for the nitrite, sometimes it takes a bit of time for the bacteria to die off/go dormant, and regrow with new water conditions, such as if added to chlorinate water or a tank with vastly different ph. usually this doesn't take more then a week or two. the real question is whether or not you have any good bacteria from the seed filter at all. if you have the time to test the tank, id ad some food to it, cheap flake would work well, and get the ammonia up to a readable level, then see if it lowers withing a week or so. if not, then the seed filter material might not have transferred well, or didn't have all that much nitrifying bacteria to begging with. if this is the case, just try adding some more, or maybe a piece of wood or rock from the established tank.
stress testing the cycle takes more time, but its a very important step when dealing with sensitive animals like coral, shrimp, or i assume axolotls. an amonia reading of 0 is esentialy meaningless unless you've had a previously measurable reading. the good news is there's nothing complicated you have to do aside from possibly adding a bit more seed material, all it takes is a little more patience. instead of the tank cycling naturally in 2-4 months, it should only take you about 1 month or less.
