Nothing special in B&W and color neg processes that would cross-contaminate each other from slightest amounts. It is just an internet legend.
Just rinse clean like you normally do.
Final rinse / stabilizer is not a particular contaminant (it's an internet legend, too). Of course, you have to rinse it off like any processing chemical. It's best to do this step outside of Jobo, on the table, simply because you have already "cleaned" your Jobo in the final washing stage of the film and you don't probably want to redo that. Sometimes I still do the stabilizer step in Jobo; in this case, I don't pour it from the LIFT system, but instead, I remove the tank, pour the stabilizer in and reattach the tank. This way, only a few drops of stabilizer gets to the Jobo processor, easily cleaned by a few squirts of water.
Rinse your reels in warm water right after development. Swirl with a dish brush every now and then.