In my experience it depends on which faction you're playing. When playing Carthage, Egypt and Eastern factions, my family members tend to get bad, money related vices much more often than when playing Barbarian, Hellenistic and roman factions. I have, for instance, never had any greater problems with wildly extravagant barbarians, greeks or seleucids, while my Parthian and Carthaginian family members seems to aquire these at an alarming rate.