I have been doing NM Dominion (aka NM Shinagawa) since around 3 months ago and I've noticed that there are some factors that might provoke the Divines to spam cannon/spell attack on you. Here are some factor that I believe will provoke them; however I don't have any solid prove to say that it's 100% accurate; especially sentences that I put in bold.
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1. Level
I solo'd my first NM Domi at lv 92, and I can tell that lv is high enough to make the Angles only use physical attack on you (normal slash, normal rush, normal spin, deathbound, ice spin, blunt spin)
On this state, the Principalies and Angles will not attack you; they will only cast heal and tarukaja or sometimes guard and counter.
This is still my mare speculation that the Angles will stop using cannon to people that is level 90 above.

2. Demon
For Damage Dealer with no Enhancement like me, Demon will usually dead shortly on NM; unless you bring the right demon (Nyar,Hacate,etc). Unless your demon is 90+, capability to null/absorb/reflect spell attack is a must because they will be spammed by cannon, magic shot, hama, and megi.
This is still my mare speculation that your demon could provoke the Divines to spam not only them with cannon, but also you
Because I've meet a melee that was on a same lv like me, yet he is always spammed by cannon, my conclusion is because of his Zhu Que.

3. Item
This maybe sounds ludicrous, but I believe so. 2 out of 3 NM where I spammed by cannon were because I brought some items that I don't usually bring.
This is still my mare speculation that some certain item like Eggshell of Avian and Messian Taraesto could provoke the Devinies to spam you with spell attack
Moreover I have a superstition that the colored egg (drop by normal Divines before NM) will calm them at NM.

4.Party Member
This is has been proven that by partying with someone leveled below 80 will provoke the Devines
This is regardless the party member(s) present on Shinagawa or not.
I’ve done a NM when I partied with lv 80 MB. We both were pwned by the cannon xD.
Moreover, I’ve done a NM when I still on party (after run) and the party member staying out of Shinagawa. I had to retreat on that NM because the Divines spam cannon like no tomorrow.
However, I just did a NM with a lv 80’s enhancer. The Divines were clam and didn’t use any Spell to me (her unicorn died because of cannon)
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Based on these proofs, I confirm that Party member will affect Devine's behavior.
Regardless your own level and whether the party member(s) is on Shinagawa or not, if you are partying with player(s) on level 80 below, you will be spammed by spell attack.

5. IRL time
This is still my mare speculation that real time affects how wild is the Divines
Need more observation; “IRL time” in this case could be Day or Hours.
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Those 5 points are just my speculation based on my experience. I don’t have any prove on that and I appreciate if you could give me more detail and fact to prove me that I am wrong/right.
I will update this post in the future if I could find more interesting findings, cheers!

Edit:
10/23/2011: Confirmed the 4th points

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