Originally posted by AlanH
I think the order is actually:
As our turn ends the improvements complete, they get their turns, then we get our turn and we then have to choose what to work on in the cities where they need new build orders.
I think it is more complicated than that, that the play/production sequence within a single turn-date is:
1) We play our turn.
2) The AIs play their turns.
3) Our production occurs in our cities.
4) The AI production occurs in their cities.
And then the turn counter is incremented, and then there's a series of checks to see whether anyone has won yet.
(And in fact we're not necessarily even first in this whole sequence. We normally are, but if you create a scenario manually where the human is not the first player then I'd expect the sequence to change a bit to match that.)
You can tell that something like the above sequence is going on because after ending our turn we see the following things happen in this sequence:
a) We see rivals' units move.
b) We get prompted for the next thing to build in each city where current construction has completed.
c) Note that during (b), you can zoom to the city which just finished producing something, then use the left and right arrow keys to visit your other cities. If you have another city which will be completing production of something this same turn, you could change its production to something else which requires the same or less shields, exit the city screen, and you'll see that the second city produces the new thing you just changed it to. So this tells us that our cities definitely do not complete their improvements at the end of our turn before the rivals get their turns. (Note: I personally think that changing production in cities inter-turn is a bit exploitive and I wish Firaxis would make this impossible. But it can be done

)
d) Sometimes after you've been prompted for the next thing to construct in each city, a popup will appear for a rival completing a wonder. This suggests that after our production for the turn is applied, then the AI production is applied.
Anyway, having said all that, I don't disagree that the production is internally happening in turn X, not turn X+1. I was just saying in my other note that the game's "feel" to me is as if production is completing in X+1, even though that's not the case. It has that feel to me because the production occurs after I see everyone else take their turn. Maybe that's just me? I don't know how it feels to other people. For a long time in my Civ3 play I just assumed that production was happening at X+1 because that's how it felt. And it didn't matter for most purposes, the distinction only matters in some very particular cases, like the culture calculator
