Does getting hit by Smoke ammo template trigger an ARO?

That's also not an ARO against an ARO.

While the original Dodge might have triggered the mine, trooper B's ARO is caused by the mine, not Trooper A.

It also only works if the mine is triggered after the first short skill, as the Dodge would be declared after the initial ARO check

 

I would like a recap of what the issue is.

 

Yes, he can declare DOdge Aro:

https://infinitythewiki.com/Template_Weapons_and_Equipment

 

Getting hit by a Smoke template is mechanically not different than getting hit by a regular or E/M template in terms of getting AROs.

Smoke Grenades and Grenade Launchers are template weapons first, and then add stuff like non lethal and Smoke Ammunition on top. The first part of that is all that ARO generation cares about.

About the other part - you never get AROs in your own turn. Which is one of the main reason why Hidden Deployment Templates are so nasty. Shooter A moves up peeking around a corner next to a friendly Trooper B.
Noctifier ARO reveals catchen them both under the template. Trooper B around the corner will have no opportunity whatsoever to FTF the template.

Only the Reactive Player gets AROs.

A Reactive Trooper is allowed to declare ARO in the following situations:

• An enemy Trooper activates within its Line of Fire (LoF).
• An enemy Trooper activates within its Zone of Control (ZoC) or Hacking Area.
• It has a Special Skill, weapon, or piece of Equipment that specifies that the Trooper can react to enemy actions without LoF or ZoC.
• It is affected by a Template Weapon, or is the target of a Hacking Program or other Comms Attack.

Also "Troopers cannot react to AROs, since only the Active Player's Orders give AROs and only the Reactive Player can declare AROs."
So no triggering AROs off Smoke AROs hitting friendly troops either.

 

In the N3 rulebook, the Speculative Fire page had as its example a smoke grenade attack granting ARO's for coverage by the template:

In his Active Turn, the vicious Dāturazi Jedak wants to crush Fusilier Angus, who is standing behind a wall, in Close Combat. In order to keep Angus from shooting him down when he turns the corner, Jedak wants to throw a Smoke Grenade over the wall. Since Angus is outside the Dāturazi’s LoF and Smoke Grenades have the Speculative Fire Trait, Jedak is able to declare Speculative Fire.

Jedak spends an Entire Order and declares Speculative Fire. Then, he places the Circular Template so that it affects Angus. Smoke Grenades are an Impact Template weapon, so Angus can declare a Dodge ARO (with his PH-3) even though the Speculative Fire came from outside his LoF. As Jedak uses a weapon loaded with Smoke Special Ammunition, and Angus reacts declaring Dodge, the Order is resolved with two separate Normal Rolls. Jedak makes a Normal PH-3 Roll (+3 for the Smoke Grenade’s Range MOD and -6 for the Speculative Fire MOD= -3) and Angus a Normal PH-3 Roll.​