Hmm, that brings up a question. How likely is it that people in-universe will be able to distinguish between the types of tiefling at all? Sure, we the players know, but how would anyone else, including the tiefling themselves? The devil's blood influencing us could be from generations past, no way for us to easily know. Maybe a learned scholar of the subject could tell, but since there aren't really major tiefling cultures, I doubt the tiefling themselves would have reason to differentiate really, and nor would most people they meet.
This does not necessarily have to be recognized by outsiders, which subtype of a Tiefling you are. In this particular context, it is more about self-revelation and empathy with Karlach anyway. Maybe one of us was plagued in the same way as Karlach. We have already escaped from Elturel, other dialogues e.g. with Rolan suggest that. Zariel also pursues the Hellriders and considers all of them traitors. How much more does that apply to other former Tieflings from Elturel?