A mini-cycle is where, after you have had a stable bacteria colony for a while, then something happens to upset the balance, like adding new fish, thus causing the bacteria to need to adjust.
In your case, if Im reading it right, everything was fine, your water stats were all normal, then you added some new fish and then your water started showing ammonia and nitrite again?
This is known as a mini cycle, it means you need to treat it the same as if you were cycing with fish-in, with daily water changes and testing until the filter bacteria colony catches up with the extra waste load produced by the extra fish. Once it has got used to the extra waste, then your stats will level back off at 0 for ammonia and nitrite as it should be. You may find this happens each time you add new fish until you have a mature filter, try to keep the adding of new fish to only once a month for a while and only a few at a time, that way the bacteria adjusts accordingly preventing the problems your facing now.