6 BLMs cast a single meteor. It's not 6 meteors being cast. What you get in the log is something like this:
Coolguy starts casting Meteor on the Badguy. (Ring appears over target's head and a blob goes into it)
Awesomeguy starts casting Meteor on the Badguy. (another blob goes into the ring still on screen)
Hotchick starts casting Meteor on the Badguy. (another blob goes into the ring)
Badass starts casting Meteor on the Badguy. (another blob goes into the ring)
Foxylady starts casting Meteor on the Badguy. (another blob goes into the ring)
Bestestguy starts casting Meteor on the Badguy. (another blob goes into the ring, and the meteor drops)
Coolguy leads the casting of meteor.
Badguy takes 43487 points of damage.
If someone else starts casting while the first person is casting, the first person's spell doesn't end until everyone else who starts casting finishes.
In other words, it works exactly like the black mages in the opening cinematic, banding together to create a single powerful spell.