I think there are a number of incorrect aspects to Servilia's ritual and suicide (leaving aside the anachronism of her death). But I'll let someone else respond to that.

What does strike me as being accurately portrayed is the Roman -- 'political worldview', perhaps? The way to "win" in Roman politics was not to kill your opponents, but to force them to acknowledge your supremacy. The best example of this is probably Sulla (whom all subsequent politicians tried to emulate). You enemies are alive, but totally unable to do anything against you but wait until you want to retire. Caesar certainly had this in mind, which is why he was so accepting of former enemies who surrendered. And why he wanted enemies like Cato taken alive and was so offended when they committed suicide.

So when Servilia takes action she does so because Atia has 'won' but she wants to deprive Atia of a complete victory.