I think anemone does not carry fish disease. However the water that come with the anemone may. If you want to prevent fish disease, just make sure you don't add any of the water to the tank. Once you finish drip the anemone, just use tank water to "wash the anemone" a few times. I would fill the container with the anemone until the water cover it, then discard that water, fill it again, then discard the water. If you do this three to 5 times, the chance that the anemone addition cause fish disease to your tank is extremely low, if not nonexistent.