A young summoner whose prayers call forth aeons and who is tasked with battling alongside them. Accepting her fate with youthful optimism, she admirably continues her fight.

—Dissidia 012 Description

Yuna is the daughter of Braska, a previous high summoner. However, she finds herself with a similar duty. She must now carry out the summoner duty. A creature known as Sin continues to ravage Spira; a sending ritual from a summoner is the only way to stave off its violence. However, she’s unaware that her pilgrimage is a suicide mission.

Thankfully, she finds out the truth early. However, the cost is her first love Tidus.

She arrives to World B, traveling with Jecht. Along the way, she and he separate. However, she meets Tidus:

Tidus: “You, uh, shouldn’t hang around here. This place is kinda dangerous.”

Yuna: “Tidus!”

Tidus: [Huh?] “Did we…meet somewhere before? Anyway. Sorry. Really gotta get going.

She remembers him, but he doesn’t remember her.

Yuna: “That’s him. No mistaking it. That’s really him. Tidus, wait!”

So when did Cosmo’s call Yuna to World B? Most likely after the events of Final Fantasy X. They defeat Sin, yet Tidus fades away to the Farplane. She remembers what he said. He’ll come if she whistles. Throughout Dissidia, Yuna whistles, hoping to meet Tidus again:

Yuna: “Wonder if a whistle would work here. Maybe in this world, he might really come running. Oh well. Wishful thinking.”

She whistles at the end of Final Fantasy X, but to no avail.

She probably doesn’t arrive in World B during the events of Final Fantasy X-2 though. She hasn’t started her new career as a sphere-hunter. While she has a dress sphere, her demeanor is still kind, honest, and polite. In all probability, Cosmo’s calls her during the events of Final Fantasy X: The Eternal Calm.