Annan used the third effect of the "Three Sirens" to control Vladimir?
This was indeed possible — especially since Annan had just used its effect to control and kill Nicholas.
Rather…
If Vladimir had said nothing, done nothing, Annan might have indeed started with the "Three Sirens" to turn the tide of battle.
Compared to the "Forgiveness of the Bone Picker," whose exact effects Annan still didn't know, the "Philosopher's Stone" which might also not be able to kill Vladimir even if used, or "Genesis Secret," which could only be used once and might harm himself as well.
Having used the "Three Sirens" once already would make Annan feel more at ease.
But it was precisely because Vladimir had gone out of his way to say this that Annan instead became suspicious. He wouldn't act rashly without clarifying the situation.
However, Annan also knew that Vladimir was not a dull person.
He wouldn't make a meaningless, bloated gesture.