Personal opinion. I think that Tav is a descendant of Charname from BG1-2. Of course that is pretty low hanging fruit, so I am probably wrong.
As far as it goes, I suspect that the artifact that Shadowhart has contains a bit of Bhaalspawn essence, and that is what is being collected. This works even if Tav isn't part of the lineage. That would be one way to tie things in with the original game, and would go a long way towards explaining why the group is being pursued/tested.
Anyway, speculation on no information.
