I think it has been said that the characters are indeed not senators. It's my understand that the attraction power of the parties only affect the over time replacement of senators as well as what faction a character will belong to when they reach an age old enough to chose a faction (at present seems to be 16).
As far as I know there isn't anything except ambitions to change the faction of an existing adult character. However the populists are a special case. If characters aren't given titles they'll drift into that camp as you say and if there aren't any male populists one of your other characters will take over the party and become leader (usually a prominent one).
The above isn't from any guide or such and is simply my own observations (apart from the point about characters not being senators, this I remember reading somewhere). So i might well have gotten some of it wrong
As far as I know there isn't anything except ambitions to change the faction of an existing adult character. However the populists are a special case. If characters aren't given titles they'll drift into that camp as you say and if there aren't any male populists one of your other characters will take over the party and become leader (usually a prominent one).
The above isn't from any guide or such and is simply my own observations (apart from the point about characters not being senators, this I remember reading somewhere). So i might well have gotten some of it wrong