Found this on http://www.ffxivpro.com/forum/topic/21701/dynamis-mob-procs/ and this is the information below:

I've compiled all the information regarding successful process's from the thread on BG forums and the thread here on XIAH into this for my LS's use. I however do not list various conditions such as day time or specific mob jobs nor do I include the type/color of process(mainly due to too much speculation) this is not meant for testing purposes, this is only a list of Reported Trigger's found thus far (some have triggered multiple colors while red seems to be the most common stagger, so I believe there is some other factor that determines color but idk yet its too early to tell):

If the mob is: RNG THF MNK BST NIN - Weakness is a JA
If the mob is: PLD WAR SAM DRG DRK - Weakness is a WS
If the mob is: WHM BLM SMN BRD RDM - Weakness is Magic

Job Ability Triggers

Warrior: Provoke
Dancer: Box Step, Stutter Step, Quickstep, Animated Flourish, Desperate flourish, Violent flourish
Dragoon: Spirit Jump, Soul Jump, Angon
Thief: Steal, Mug
Samurai: Hamanoha, Blade Bash
Scholar: Libra,
Monk: Chi Blast ,
Corsair: Earth Shot, Light Shot, Ice Shot,
Ranger: Bounty Shot
Beastmaster: Dipperyuly: Spiral Spin
Summoner: Garuda: Predator Claws

Weapon Skill Triggers

Dagger: Rudra's Storm, Evisceration, Shark Bite, Mordant Rime, Mandalic Stab, Mercy Stroke, Cyclone, Energy Drain, Aeolian Edge, Dancing Edge
Katana: Blade: Jin, Blade: Rin, Blade: Hi, Blade: Chi, Blade: Ei, Blade: Ku
Hand-to-Hand: Combo, Victory Smite, Ascetic's Fury, Tornado Kick, Asuran Fists
Sword: Sanguine Blade, Red Lotus Blade, Chante du Cygne
Polearm: Skewer, Drakesbane, Wheeling Thrust, Camlann's Torment
Great Sword: Scourge, Ground Strike, Catastrophe
Scythe: Shadow of Death
Great Axe: Ukko's Fury, Raging Rush
Axe: Spinning Axe
Marksmanship: Numbing Shot
Great Katana: Tachi: Fudo, Tachi: Gekko

Magic Triggers

Black Magic: Fire, Thunder, Blizzard, Fire II, Stone III, Water III, Fire IV, Blizzard IV, Thunder IV, Aero IV, Blizzard V, Stone V, Stoneja, Frost, Bio, Bio II, Sleep, Sleep II, Sleepga, Sleepga II, Stun, Dispel, Bind, Blind, Blind II, Drain
White Magic: Banish, Banish II, Banish III, Holy, Flash, Dia II, Silence, Slow, Slow II, Paralyze, Paralyze II,
Blue Magic: Fire Spit, Head butt, Lamb Chop, Quad. Continuum
Ninjitsu: Hyoton: Ni, Raiton: Ni, Doton:Ni, Hojo: Ni, Katon: Ni
Songs: Magic Finale, Horde Lullaby, ??? Elegy, Foe lullaby, Foe lullaby II
Avatar Blood Pacts: Carbuncle: Holy Mist

these are all the staggers found up to page 21 on BG forums: Neo-Dynamis thread

and up to page 17 here: FFXIAH Dynamis Nothing Drops