The moon never sets, even if one half of the world doesn't see it, they will eventually, and since a very small portion of the world, all of which is now in the current location of the MT know of MT, they can't warn the others. It was never stated it envelopes the whole world all at once, it could be a process.
Thats how i see it working too. And remember Tomorrow is still narutos birthday. So im sure they'll have to beat him b4 the whole world gets a glance at the moon. On narutos Birthday.