There is also the situation of the fish in your established tank existing quite well with something, and not being affected by it due to a stronger immune response. Stress lowers a fish's immune response, making them susceptible to diseases. It is quite likely there are bacteria, protizoans, a whole host of things that your established, healthy, stress free fish are exposed to, and their strong immune response is keeping at bay.
Take your new purchases, stressed from being caught, bagged, transported, put in a tank with strange inhabitants & perhaps different water parameters, and you have stressed fish. How long before this stressful event they were exposed to the same thing when purchased by the shop is often unknown. You expose them to pathogens your healthy fish keep at bay with a strong immune response, and bam, sick new fish.
So your response is to med the whole tank, healthy fish as well as ill. The healthy fish have a strong natural immune response, the best medication nature can provide. You med them, making this strong immune response unnecessary. The natural immunity lessens, and the existing fish now are susceptible to a pathogen they previously fought off quite well, without any chemical intervention.
Which came first? Did the new fish make the existing fish sick? Or did the existing fish make the new fish sick, your efforts at a cure weakened the immune response of the healthy fish, and they in effect made themselves sick? How would you find out?
You would find out by dissecting a series of each fish, before exposure. You would do smears and stain slides, examine with a microscope, and compare. This would also give you a more definitive answer as to what medication to use for the problem.
Doesn't a small tank, filter, & heater sound easier?