The nitrite-consuming bacteria are slower growing than those that eat ammonia. Seems likely that the introduction of the fish caused a boost in ammonia that the bacteria wuickly caught up with, and the nitrite consumers are just lagging a bit behind.
If your test kit only reads to 200, anything above that is guess work. Could have been 250, could have been 500. Which means that doing water changes until it drops into the readable levels is the only way to know how much is in there. Since it seemed to rise after the water change, I would test the source water. Even if everyone says their water is perfect, I'm paranoid and would still test it myself to be certain.
If your test kit only reads to 200, anything above that is guess work. Could have been 250, could have been 500. Which means that doing water changes until it drops into the readable levels is the only way to know how much is in there. Since it seemed to rise after the water change, I would test the source water. Even if everyone says their water is perfect, I'm paranoid and would still test it myself to be certain.