My limited reading says that the cistern should be drained and cleaned, and the opening where the animal came in be covered/screened. Cloroxing the cistern is apparently NOT the proper way to handle this particular problem. In fact, some animals are 'welcomed' in a cistern.
What you can do is search the WEB with your favorite Search Engine for a cistern and you'll get over 1800+ hits on WEB pages talking about 'a cistern' (It's cistern; NOT sistern.) There are cleaners for your cistern from what I've read. And again, properly seal off (or screen off) the opening where critters can enter your cistern. Mostly, they enter from vents.