Even your own cities do not all convert automatically. One thing that seemed to work is to have one of the higher production cities do nothing but make missionairies for a while, and send them off to all possible cities - including your OWN if they don't show the little religion icon.
I was able to convert two other civs that would be otherwise hostile to me that way.
I was able to convert two other civs that would be otherwise hostile to me that way.