There's a couple of contradictions.
I'm reading that Tamaki created it after he lost his games in the Earthquake. And he created Carnival Corpse for fun.
I'm also reading that Hagire Rinichiro created it after the earthquake and after taking over the old man's body. That old man was supposed to be the previous winner of Carnival Corpse but how is that possible if Carnival Corpse was only created after Hagire took over the old man's body?
Then there's the question of when he took over Toto's body. In the later chapters (50+) it shows Toto with his original personality and his original clothes (with the vest and pants instead of the gown he wears now) asking why he's not fighting the Wretched Egg and Hagire telling him he's going to take over his body.
But the first time we see Toto during Ganta's time in DW, he seems to have switched over his clothes and personality (wearing the gown) already. We also see old man Hagire talking with Shiro.