Last night our alliance beat Promyvion Dem 2/3 times!!! We used a very simple strategy of kiting the mob and having everyone immediately kill the offspring as soon as they popped. Almost no one in our party got into the yellow more than once.
If you go to Promyvion Dem remember these key tips:
1. KITE THE BOSS - just like you're flying a kite. Provoke then run in a circle around the arena. If you're playing NIN or /NIN have your party tell you when the mob goes after your RNG or mages. Recast Utsusemi and provoke again.
2. BRING RANGED DD's - RNG is the bomb in all these BCNM's. BLM's don't do great damage vs. the Dem boss so have them attack his offspring and heal you.
3. BRING A RED MAGE - Have the RDM sub BLM and elemental seal + GRAVITY on the mob to make it easier to string the mob around.
4. At 20% BOSS HEALTH UNLOAD ON IT - SMN, RNG, BLM 2 hour and nuke the crap out of it. Our SMN's 2 astral flows pretty much killed it outright. She used Titan which did awesome damage.
Follow these steps and you should do just fine.