If your compost bin is separate from the gardening area and if you only add compost that has been thoroughly decomposed, you shouldn't have any problem with disease even if the onion or potatoes included actually had a disease. The heat factor, the abundance of microorganisms and the lack of host material all play into this. There are some pathogens that might lay dormant for unknown periods of time in average soil, however a real compost bin is not a friendly place for life that thrives under average conditions.
