That's a fun lapsus

Oh yes, I meant Terra Indomita. Thank you.

If you mean Terra Indomita, it probably does, but it does not impact any of the new tags added by that mod.

Does it work with Terra Invicta?

Okay, thanks for the clarification

The latter. I think the capital choices were made with some sense, such as Apulia's only city, Barium, being their capital despite being outside the Apulia province because it's still technically Apulia, it's just their only city (probably with historical background to justify that) and as such it is the capital.
As you said, it's to correct mid-game unavoidable inaccuracies such as releasables not having the right capital.

Is this for nations at the start as in some nations start the game off without their namesake city being their cpaital? Or is this for when they have a war or revolt/rebellion and end up with a random place place being their capital instead of their namesake city? I do notice it a lot especially when you liberate places their capital will be random. I liberated odessos (the country) for example with about 5-6 states within their borders and instead of odessos (the city) being their capital, it was a random state with no city, kinda dumb.