Right. Can we get a confirmation on if shrines do or don't function the turn they are made? I wasn't sure but I figured that you wouldn't be able to do labor in buildings your building that turn because of order of operations, but wasn't sure since the shrine doesn't seem to take labor and the consumption of luxury goods and changing of moral seems to happen after or between turns?
Also are you able to use irrigation on the same turn that you make it? Since it doesn't take resources to irrigate, maybe? But unsure and also Toaster did his turn assuming you can't I think.
Shrines do not function the turn they are made.
Most tile improvements do not function the turn they are made.
Sorry for the confusion. You're right that by Rules As Written, they should work when they can slot into the turn order. But that opens a confusing mess of edge cases where some buildings work immediately while others don't, and none of it follows common sense logic, so we'd have to work through and figure it out again repeatedly.
Granaries and Warehouses will work immediately. Resources shouldn't decay instantly, and the decay for unstored goods can reasonably wait until the end of the turn, after they're built, before it happen.
Palisades, Walls, and other such defenses will work immediately. Military battles take place in a special sub-turn after the main turn, which means the walls should be done enough to work.
The only other thing I can see in the current build lists that should do something immediately is the Explorer's Hall's ability to proc an exploration event. Eg, "The new master of the Explorer's Hall reports that he and his family immigrated to the city recently from a village upriver. They left because food was getting scarcer every year, you should look into that before they turn into bandits from necessity."