The ARC moogle switches targets periodically on his own. I don't know how he chooses his target. Might be random.

Both the WHM and PLD moogles can be called for help by other moogles. The King can also be called for help, but maybe not until after he has absorbed the fluffy white soul of either WHM or PLD moogle.

BLM does his own thing no matter who he has hate on, so no point worrying about him. I'd say the same for BRD and THF moogles.

So when kiting, your main concern imo is MRD and King. That's it. MRD is easy to get and keep on you. King is easy to get on you, but you have to be ready to get hate back later in the fight when he is called for help. When you're comfortable with those two, then you can try to keep some of the attention of ARC or PLD.

Because moogles are smarter than your average zombie and will not mindlessly follow a kiting tank (except Ruffletuft, so take that Warriors!) the other members of your party have to watch out for themselves. That means BRDs and WHMs in particular will have to use their hate shedding abilities and kite for periods of time. They also need to watch their hate in the first half of the fight. It does little good for a cocky BRD to outdamage everyone else in the first half just to die to a mob of moogles in the opening minute of the second half. Better to share the hate with fellow damage dealers.

Take a look at the abilities PLD gets. None of them are particular useful in a kited fight. GLA on the other hand has access to Second Wind, which is very handy. And Decoy, which can be nice for Eagle Eye Shot. So, you might want to "/job off" for moogle fight.

Lastly, since when you get down to it, you can't kite a string of moogles while the party picks them off one at a time, you might be better just straight tanking the tankable moogles on PLD (or WAR) instead of kiting. But either way, it isn't necessarily the tanks fault if a WHM or BRD goes down to a rogue moogle.