In his bio, nothing is said of CSZ's consciousness being part of what makes him him. You could say that this means that either the CSZ variation simply doesn't exist in his story or that Triborg uses CSZ's kombat data without actually integrating SZ's mind into his consciousness.
As for how he "splits", it's more that it seems like he is simply able to control multiple bodies at once. Definitely not unheard of for AI-based characters in fiction.
But really, details on Triborg's nature are generally pretty sparse. This is all speculation.