I finaly encounter a group of the Aldmeri Dominion and they started to attack me so I killed them all and loot thier body but ther's one thing that I notice "Justicar Excution Order" and it's saying that I disrupted thier operation and great harm.(This happen after I play Dawnguard)
Anyone encounter this before?

All the time.

However, it's apparently random when they will attack. Even though I usually only get them after the Diplomatic Immunity quest and/or raiding their Fort Death Camp way up north for the Grey-Mane rescue mission.

I had 3 random Thalmor attack me but they didn't have an execution letter and I didn't tell them that I worshiped Talos

Had this happen a few times.

I've had that on... one character, I think. Might've been two, I forgot.
Ivory the Argonian looked so awesome in Elven armor it made the Thalmor jealous.

This might explian the reason.

When I say random, I do mean random. You could get a hit squad sent after you in the first 10 minutes of the game after escaping Helgen.

The Thalmor with the "Execution Order" are just a Random Encounter. I had a character who went straight to Markarth get attacked after escaping from Cindha Mine.
I had a character cast Oakflesh near Helgen and get attacked, but I may have looked at Elewyn funny during the carriage ride into Helgen