Thats because the mod names it's characters like vanilla characters so theres no clean way to identify them and tell them apart.
Apparently the mod has it's own system for identifying characters, for whatever reason, which isnt really compatible-friendly at all.

Update: The latest update to their mod gave them unique names, so they should work now.

That's super nice to hear, thanks a lot again man!

They changed it back btw, so yea....dont expect this characters to work consistently, since they dont seem to know what they want to do. Every character in the workshop has a unique name and the chadentified by that names, since UIDs are dynbamic. Tarnished characters use the exact same names as vanilla and, apparently, even go as far as to change this names on the fly...so it's simply not a reliable mod to support.

tl;dr: they may or may not work depending on what the authors of said mod do, it's not up to me at this point.

Oh no why did they do that :( That could be fine tho, they actually use their own system to display completion marks in their custom character selection screen so not having them during run is a lower inconvenience. I'll ping them in their thread to try to let them know

I already did, apparently it was a mistake but we shall see...as you say tho, they do have their own marks so it's not that big of a deal.