Spoiler:
Remember, this wasan't exactly a subtle thing. bahamut didn't just pop out of the sky. First the children were taken, and everyone had been astir about that for at leasta day, and then Kadaj, Loz and that other asshat all had the kids stand in a circle around town square, and then a bunch of monsters came and started eating people. Also, remember on cloud's phone they called from Wutai asking about the children. I imagine something similar happened to all of their hometowns, and naturally following the children lead them to midgard. Once giant beasts started eating people, they probably all figure out something must have been happening in the town square.

They suddenly knew about the sephiroth thing because vincent told them, vincent figured it out because of his dark all knowingness , as well as his having seen them alot in the ainchents' city and being connected to the whole sephiroth thing.

Tifa coulden't even beat Loz. All of them conbined coulden't even really hurt Bahamut. So they coulden't even really hurt. And how was the world at stake? You get into the AH he has to win this fight ahhh!!! mode in movies, but really what would have happened had he not won? Also they weren't sure of when if ever he would turn into Sephiroth. But even with Sephiroth back, nothing too amazingly bad would happen. They were also watching so they could jump in if need be.

The movie has alot of intricate things that you have to watch for. Like Cloud was attacked, initially, by kadaj and his guys because Rufas told them that he had it. And Tifa does NOT have pokey nipples, they are the seams of her vest. Attention to detail is very important.