BioSpira is the beneficial bacteria that you need to cycle a tank in liguid form. It is poured into the tank, where it is free floating through the water. It can, and does begin to process all the ammonia/nitrite that it comes into contact with as it is floating in the water. Given proper circulation and time, with a good platform (sponge, bio-balls, ceramic rings, lava rock, etc), it will settle and colonize the bio-platform in the filter as well as some attaching and growing in the gravel and on the ornaments of the tank. Until this attachment and colonization occurs, though, the tank is not really cycled. It has the bacteria, but it is not a fully functioning bio-filter. Free floating and processing, though, the BioSpira can give the impression that the tank is fully cycled. In a tank of tropicals or a very lightly stocked goldie tank, it will move to full cycle without any bumps or problems.
Typically, it takes about 2 weeks for the bacteria to colonize. Once it does, it can begin to grow a population of beneficial bacteria that is large enough to process all the ammonia/nitrite in a tank. It can, and does, process as it is colonizing, but if it is given a large amount to process, it may not be up to the job.
Did you change the water at all in this time? If you change the water too soon, you can be dumping part or most of your beneficial bacteria down the drain with it.
If you have any nitr
ate readings (and none in your tap water pre-tank) then you have
some beneficial bacteria working for you. Since you say greater than zero, but not a number, I am going to assume that it is a quite small amount. Since there are ammonia burns on the fish, I am going to assume that it probably was more during the week. I would then conclude that the tank is already bouncing back from a bump in the cycle - the BioSpira is beginning to colonize and really work.
I think, unless the water parameters are truly AWFUL, that I would give it a day or two more, or change the minumum amount of water needed to keep the fish healthy. Do not disturb the filter, cartridges, sponges, etc. at this time. I bet it is fully cycled within a day or so - and was only bumped by too many fish, too much food, a water change or simply not being totally colonized yet. You may never have the exact answer as to why.
That tank is cycled - it just is not quite up to the job of handling your fish's waste. It should be within a day or two. Your fish should bounce back quickly.