I have the same problem that the city doesnt consider the tile gained from a Dun Cinneadh a part of the city until you actively click it from inside the city view.
Good to know I'm not imagining things. That said as noted it's not really a problem if you are into micromanagement of the city, if you let the AI run the city tho they are basically dead tiles, as it's just two clicks and you are working it if you like to.
I'm not sure how the border code is but could it be that the tile just get added to the empire and not assigned properly to a specific city? So it just sits there in limbo. Cause it looked real weird when I had built some Duns and then Askia came and took my city away from me and there was all these little Dun zones spotted about that didn't swap to him but remained with me dotted around the city.Perhaps they are all considered to be or attached to the capital?
Yes I noted the free unit xp thing to. A free unit in the capital got one promotion even tho the city had Orders (+15), Barracks (+15) and Armory (+20). A built unit gets two promotions with that. The one that spawned for free only got 75 xp. The once that are hard built get 150 xp (with this setup of buildings etc). So it's more like they are being purchased instead of built or spawned.
The Shiltron (next to another one) with a a couple of cover promotions is basically a wall. The AI doesn't know what to do with it and tries to walk around it. The cover, the extra healing, the retribution damage ...