Once your tank is cycled if you are treating your tap water with prime the ammonia in your tap is really not a problem because it will be converted to ammonium and will be handled by your bio filter (or plants, if you have any).
My tank will test positive at .5ppm for ammonia immediately after a WC but it's back to 0 after a day or so. In my case I have chloramine in my tap water.
Watch your nitrates as well.. sometimes in this scenario those can start to build up because you're effectively "adding" more ammonia to the system than would naturally be involved and water changes don't have as much of an impact on bringing down your nitrates as they could.