I think Yuna didn't actually know he was going to appear there, she says she is going to home to the three leaders, so she was heading to Besaid anyway, when they spotted him from the Celcius I theorized that Yuna ordered Brother to land immediately.

As for the mass of the people on the beach? Maybe a welcome home party for Yuna? How did they know? It's possible that Yuna contacted Lulu and Wakka on the comm sphere that she was coming home, just a theory.