When Tartaglia (then known as Ajax) was 14 years old, he was drawn into the Abyss and re-emerged greatly changed by the events that transpired there, he gained unmatched combat prowess. His father, who was worried he would bring unnecessary attention to the village of Morepesok, brought him to the Fatui in the hopes that they could hone his temperament, only to watch as his son easily beat up well-trained soldiers. This piqued Pulcinella's curiosity, and they conscripted the boy into the Fatui under the guise of serving the Tsaritsa as punishment.
Little is known about Pulcinella's personality, but they appear to be rather calculating: they correctly predicted that Tartaglia's immense strength and habit of being in the midst of chaos could be used to advance the Fatui's cause, while sating his appetite for battle. Pulcinella also gives "cautious counsel" regarding Tartaglia, calling him trustworthy but warning against growing attached to him.
(To be added)