Ace uses luck to his advantage in battle. Thanks to how quickly Cut Cards charges, he can constantly fill out his hand and play cards to support his allies or activate potent attacks. Draw early and often to have your gambits pay off!—Character Selection description
Sometime after the 12th/13th cycle…
Ace is the card weilding cadet of Akademia. One of twelve children adopted and raised as human weapons, he and his other Class Zero classmates save the world.
When did Materia call Ace to World B? Most likely before Ace dies. After World B, he arrives to either the timeline where he dies or one where he survives the war. The second live timeline splits, as either, he’s alive studying in a library, or revived from the verge of death.