Shoot = Ranged attack Vashj does to the top threat if they are not in melee range. It will 1 shot anyone who is not a tank typically.
Multi-Shot = Ranged attack Vashj does to random players and will hit other nearby players to whoever was targeted. This is unavoidable but it is survivable for everyone as long as you aren’t hit by other damage like an unlucky spore (people may have to wear slightly higher stamina gear to survive this if they are cloth… it does around 9-9.5k dmg on cloth).
You are getting these two attacks confused.
In response to the OP, you are correct… the threat drops always occur after a persuasion is cast and it seems likely to me it happens when the tank is targeted by the persuasion but isn’t actually mind controlled (perhaps from a resist or a grounding totem). Fortunately, Vashj is tauntable so you can easily have another tank who is 2nd in threat or who can taunt the boss immediately after the threat wipe.