So the supposed "genocide" commited by Republic (or even Jedi) didn't actually happen? (The timeline videos and some NPCs in the game seem to imply this genocide.)
I believe the "genocide" they are referring to is the Republic invading Sith space. After the Great Hyperspace War, the Republic went into Sith space to exterminate the Sith and prevent another war.
So, yes, the "genocide" did happen. But it had no real consequence as the true Sith threat had escaped.