Probably, a better way to put this is: When the weakened form of Domination magic wielded through the Helm lost its grasp, the natural soul remnant of the Undead in question was able to express itself.
(The other modifier for control is the use of Scourgestones. Remember we found new ones in Icecrown before going to the Shadowlands.)
After the Maldraxxus revelations about Necromancy it’s just part of the magic that a soul is required to animate the body, or construct. (In some cases, multiple souls.)
All sentients raised as Undead will have some part of their sentient soul kept to actually power the body. Removing the souls from the Shadowlands is a big hole logically, which might be explained by either “real” Necromancy functioning in the Shadowlands, or, our not knowing the actual villain(s).
(TBH, TimeyWimey is probably the best explanation, though it’s not used: Time works differently in the Physical Universe compared to Shadowlands, so Necromancy practiced from the Physical Universe has the effect of grabbing the soul from multiple points in time in the Shadowlands, contributing to the damage a soul sustains.)
Add to that the Conductor quest in Bastion, where souls are not passed to the Shadowlands by the Kyrian when a “master”, or Valkyr, calls them (Necromancy). (Yes, I know, they return another to life to kill a Necromancer.)
I still think, in many cases, Necromancy on Azeroth needed to prevent the raised from having a complete soul. So partial souls should be assumed, and thus meshes with the description of changed emotional perception (Angry, etc.).
As to the Plague, people shouldn’t forget that a Ghoul bite can infect.
Right now I think it safe to assume the Plague is from the House of Plagues, carries Necromantic reanimation as part of it, was moved via the Dreadlords to the Legion, and then was used on Azeroth.