Sometime after the 12th/13th cycle…
Vayne is the son of Gramis, the Archadian Emperor. Through Machiavellian tactics, be becomes Consul to Dalmasca. Like Gramis and Gabranth, he’s amoral and completely ruthless. Vayne also conspires with Venat, a renegade Occuria, who promises to make him Dynast King.
When did Vayne arrive at World B? According to the Wikia:
This means that either Chaos or Spiritus could have called to World B. However, whenever this happened, Vayne has the ability to transform into Vayne Novus, Vayne’s second form. This happens as he uses the nethicite to transform, but before merging Venat to become The Undying.
The most likely scenario for Vayne’s arrival is sometime before Vayne’s final form. Once Vayne returns to Ivalice, he returns the heat of the battle.