Unexpected quest success

I passed the "build X colosseums" quest, by conquering 3 of my neighbours. Number of colosseums actually built: 0. Unfortunately, this has the downside of number of colosseums affected by this quest: 0

EDIT: Actually, nevermind, they are affected. I thought cities not actually founded by you were unaffected by quests such as these. I was almost certain of it, having , I could have sworn, seen things like newly conquered cities being unaffected by bonuses to harbours from harbour affecting quests (think there are 2 if I'm not mistaken), etc. Weird. Anyway, works out for me.

DOnt coliseums produce culture?

Generally, colisseums do not produce culture, though this quest reward can make them produce culture (which would actually be pretty good for when you take over new cities, similarly to new cities producing culture from terraces, but much less reliable than the terrace).