In a word yes but you do need 'some' ammonia to get your system working < 1ppm should be OK, if you are really concerned what is your water pH? although filter bacteria prefer 7.5 to 8 or so ammonia is more toxic at this level, if you filter over some peat to reduce your pH to below 7 more of the ammonia will change miraculously into a less toxic form (NH4 instead of NH3), it shouldn't impact too much on the cycling process, but how are you doing your Ammonia testing? sticks or a liquid test kit?
If you aren't using a liquid test kit then now is the time to invest in one.
Have you tested the ammonia level in your tap water?? - are you on a water authority supply or a borehole of your own? what is this 'filter' you mention? - it wouldn't be a water softener would it - they are a darn menace as far as fish keeping goes (too much sodium hydroxide / salt in the water), you need to get an unfiltered / untreated feed from before it if it is - either way I'd invest some time finding out what it is and what it does.
If you have done such large changes of water then with only three fish I really really really don't see your Ammonia remaining at toxic levels at all, a 75% change should have really dropped the ammonia down, at 4ppm do a 75% water change and I would expect to see 1ppm or better - something else is going on here, nobody is using one of those stupid antibacterial sprays or something nearby are they? - or even diligently cleaning the tank with some other nasties.
Tetra Aquasafe should deal with Chloramine or Chlorine and the ammonia too , there are also two others available though not quite so readily they are AquaScience Ultimate and Seachem Prime.
If you want a good source of water catch the rain, once your tank is matured you won't need that much to stay on top of the nitrates etc.