Overthinking Things.

For Legion to kill his parents, Litori's ancestor recommended to the Supreme Alliance that Salvini be used as bait for Legion.

She said that Legion hated her for taking his title and sullying his name, so he is likely to do everything in his power to kill her, even if he suspects a trap. The Supreme Alliance didn't believe it at first because it sounded like childish hate. 

They expected more from Legion, but they had to change their minds when proof of Legion's efforts in the recent war with the Vipers and his attack on Salvini was displayed. 

So the Supreme Alliance used Salvini as bait. Legion took it because they thought they were one-upping the Supreme Alliance. They didn't know that the prospect of cursing the Supreme Alliance was also bait.