Sorry "emperor". Not buying it.
Even if you wanted to make humanity progress by science and technology the genocide of witches is not necessary. The moment tech advances enough to surpass magic is the moment witches lose prominence and importance and people turn to tech for their problems. Is a natural civilization development that can be seen in our world, when people turned from misticism and faith to science.
So no, genocide WASN'T and ISN'T justified. The situation you have now is a direct consecuence of that. However, the girl has some speck of truth. People are like sheep, and if a carismatic leader says that the world is flat and giving your first-born to be sacrificed is right and just they will follow, specially if you support your claims with enough physical force. As before, has happened before in our world and is still happening. If I were the boy, i would have gone directly to the imperial palace and HQs and nuke'em.
@nachtness: And not even then. The Imperium would have investigated first the witches' power sources and sent them to the Psykana if found uncorrupted.