The Dunyain see many posibilities, thousandfold thought ok. But that doesn't seem to fit with trying to kill him outside the Ark, if they meant to use it to start Resumption. And they didn't expect that Full-Ajokli, I think. They don't forsee everything.
I don´t have the book but I re-read that sequence yesterday: It´s birth, Kellhus hologram descending, silence, wail, and the narrator tells the second birth was mercifully quick, Esmenet put away the blue baby (paraphrasing) and Achamian never knew about it. Ok, he didn't say when that second birth took place, but he describe it in that scene. I understood it took place then, but you can read that it had happened before.
EDIT: thanks Madness
No, I don't think they expected Ajokli I doubt they necessarily expected to find Kelmomas either. But still, I think the idea that they would have preferred to kill Kellhus and use another Anasurimbor is plenty fitting, if they could. It would have still fit with the Celmoman prophecy.
As for the scene, so I'm looking at it right now on Chapter 19.
Achamian is sitting on the corpse of a Bashrag, thinking about the fact he has a son from the first birth.
The Quya attack the Scranc in the Canal, slaughtering them.
"It flees!" some Longbeard cried from the parapets above. "The Horde! Fleeeeees!"
Bunch of dudes are all cheering.
It mentions the second birth being mercifully quick and that Achamian would never know what became of it, the dead twin. How Esmenet gets rid of it.
Achamian gets off the dead Bashrag and sits on the thing's head.
Section break.
Describes the scene again with the fallen horn. Nansur Columnaries and Eumarnan Grandees watching Scranc fleeing.
General Inrilil ab Cinganjehoi yelling how the Soulless bolt from the wrath of the Souled.
Notes how many (more than a million) corpses are around.
"Then the keen-eyed spied Him, and jousting cheers became a tempest of ecstasy and adulation. The Holy Aspect-Emperor stood upon the Vigil, high on theon theward face of the surviving Horn."