If these worms are passing out of the rectum. The most probable cause would be a tapeworm infection. The adult tapeworm stays in the intestine, but passes segments with eggs sacs in them (these segments can move). Cats have two ways primarily to become infected with tapeworms, one is by ingesting fleas, and the other by ingesting mice. Here is a link with a great deal more information about the tapeworm life cycle. tapeworms
There is no effective home remedy to rid them of the adult worm, but there is an over the counter medicine that can be used and is found at pet stores. Make sure the product contains the ingredient called praziquantel as stated in the link provided above.
Your other cats should not be at risk of becoming infected from him. They cannot pass the tapeworms to one another without it going through the secondary host (the mouse or flea), but it will not hurt them to treat them, even if they are not affected.
I hope this is helpful. Please let me know if you have ANY other questions. My goal is to give you 100% satisfaction and if you are not yet satisfied, please reply so I can clarify for you.
My posted replies are for general education only and not meant as a diagnosis. Only after a thorough veterinary examination can a diagnosis for your pet be made and specific treatments be advised or medications be prescribed.