The California Department of Fish and Wildlife (CDFW) and various bird rehabilitation organizations are recommending that people in southern California stop feeding birds until April or May when Pine Siskins have left the area. Even though there have not been many cases here (compared to Northern California), they are being cautious. In any case, feeders should always be cleaned regularly, along with the ground below the feeders. Salmonellosis is transmitted mainly through the accumulation of droppings around the feeders and birdbaths. CDFW recommends draining birdbaths as well, but an alternative would be to clean the baths out at least daily.
The no-feeder recommendations do not extend to hummingbird feeders, but those feeders should also be cleaned and sterilized regularly as standard practice.
Pine Siskins have been in the Los Angeles region in small numbers this winter (with larger numbers in a few areas), but most people do not have them at their feeders. However, this disease is known locally from Lesser Goldfinches and other finches as well.
So in summary, it is probably most prudent to stop feeding birds for the next month or two, but if you choose to continue feeding, make sure the feeders and surrounding areas are as clean as possible.
—Kimball Garrett