Tris' lynch basically shows that players push on reads without out mechanical info since the entire Tris push was read based. But town having very good reads isn't foolproof. They could catch scum 9 times out of 10 with their reads this game. Not the one mislynch that would invalidate it.
Emilia's ability wasn't the only thing that screwed Rej over completely, because the fake IC was built to be a choice, not an obligation.
If scum were only going to use the fake IC to ride for town cred, then Emilia's ability was built to counter it. It was always meant to scum lock the player, or at least put suspicion his way.
So Emilia's role being in the game to counter it, would have been null, if the IC happened after she had been taken out.