I am going to have to side with Joasia on this one.
The idea of the sins of the ancestors being passed down was a creation of ancient Greek culture when they tried to explain why it was that evil parents had successful children. Why do the wicked prosper?
They tried to encourage morality by suggesting that there was no escape from the misdeeds of previous generations, and that even if that was not immediately apparent, it was surely imminent.
I believe it was Hesiod who stressed this idea.
I think the concept of "original sin" is therefore something the Romans inherited from the Greeks.
If my recollection of classical history is wrong, I hope someone will correct me.