The citizens of Elturel swore a sort of oath-of-alleigence that required them to defend the city. This oath was corrupted so that the citizens had unknowingly sworn themselves into Zariels service.
So it seems that it is possible for Karlach or Anders to have been bound to Zariel without their consent.
Interesting idea.
Anders I am sure sold his soul outright. He even says so when he’s caught in his lie.
It’s possible Karlach was caught up in the oath but her story suggests she was fighting the blood war for quite some time. And it doesn’t explain why the other tiefling refugees aren’t targeted personally by Zariel.
