In a normal Windows environment, such tasks are handled by 'modal' dialog boxes. That means when they pop up, they have their own message loops that stop the main UI thread from continuing until the user gives a response. In a game where things need to be animating and so forth behind the dialog box, you either have to all the static UI stuff in its own thread, or you have to use 'modeless' dialog boxes which operate like separate mini-application windows, which unlike modal dialog boxes, have the capability to pop up willy nilly in any kind of order.

If they can't use modal dialogs, they need to fake this somehow so there's a queue of needed responses before other things happen. Right now they're just throwing up dialogs when there's a need for one detected. Technically it all works out, but it is kinda confusing to deal with the most recent message before the older ones.

This is one thing that Civ 5 did REALLY well. The notifications that required attention came up as icons that you could deal with sometime during the turn, but not right away. The ones that you had to deal with still blocked your turn from ending until you took care of them, but they didn't pop up right away and interrupt what you're doing (or pop up and interrupt dealing with another popup).

It's probably too late to do that in Elemental, but they could reduce the number of things that spawn a popup which itself would alleviate the problem.