I want to add that hate works differently in this game than it does in FF11. In FF11, as long as no action was taken against the aggro/linked enemies, they would keep attacking their target and not get hate on anyone healing. In this game, understandably, healing any target that has enmity on that enemy would give you hate like normal. So if your puller gets a bunch of links and you heal them before anyone else has gotten hate on the adds, you are going to be taking hate.

Your party should be splitting up to take care of the adds. Tankier characters (Gladiators and Marauders, occasionally Pugilists) should be holding their own enemies each and building up enmity while the rest of the party gangs up on enemies one by one, either that or have your party split up into units to take care of each add. Provoke and/or Flash should be more than enough hate to prevent enemies from going after you immediately, as long as you don't overcure and possibly stick with Cure initially instead of Cura. As Raldo suggested, keeping Stoneskin on your party as much as possible will help immensely.

Also another note, don't think you have to go with an exact "X Healers, X tanks, X DDs" setups. As long as the party is flexible and everyone has access to some way to heal themselves, you should be able to make do with whatever is available. All the classes are quite versatile. For example, CNJ is the designated healer of the game, but most people underestimate its ability to nuke with aero and stone spells. With Cleric stance up, your damage is actually really high.