don't stand so close

So, the Dead Three did not, intentionally, start murdering primordials for the purpose of becoming gods and steal their power (they still stole the power of the primordials they slew as mortals, but the goal was not to become a god).

First and foremost they were tortured by Jergal in their sleep, because Jergal saw the primordials as threats to his revised Ascenion ritual (with which he sought to be reborn as six divine entities and in so doing make sure that the Disjunction never happened). So he plagued the dreams of Myrkul, Bane and Bhaal with traumatic nightmare visions that revealed to them the locations of the God-slaying weapons they would use (mostly Bhaal because he was their killer).

Anyway, skip ahead a few years and Jergal abandons them after they banished the primordial Maram because he thought the threat was dealt with. Which leaves the Dead Three to their own devices. Of course they get the bright idea to release even more primordials into the world and one of them was called Torath of the Obsidian Vault.

All primordials hail from the Elemental Chaos and have an element associated with them: For Borem it was fire, for Camnod wind and I will take a daring guess and say that Torath was connected to the element of water.

Anyway, Torath, along with two others, got subdued by the Dark Three and commanded to raise an army in their names, which the three primordials did.

Torath assembled a giant Kuo-Toa army from beneath Mount Throndor in the Eastern Dragonspine Mountains (modern: West Galena Mountains).

So... given that the Dead Three had a habit of splitting the tasks between them I would take a guess and say that each of them personally oversaw the actions of one of the three primordials.

Given that Tyranthraxus the Flamed One preferred the shape of a dragon and is connected to fire (and, apparently, partly to lightning), I would say that Bane was the one to command this primordial directly.

Myrkul, most likely, took control over Edranka of the Smoldering Haze because he was the one to sniff out Hargut and Haask. It would make sense if he took it upon himself to command Edranka to wage war with them.

Which leaves Bhaal with Torath and his army of fish-people.

I am no longer surprised that Bhaal doesn't get pissy about Durge getting worshiped as a god by the Kuo-toa, but only about becoming the chosen of a redcap.

Apparently, he approved of Torath's fish-army. And if Durge tells the Kuo-toa to assemble an army in their name? And to worship them as the god 'Mahkloompah'? That just echoes what Bhaal himself did.