Unless they fix it so that pop-ups are FIFO, such that the oldest pop-ups are on top, this is a recipe for garbage UI outcomes, the kind of thing where pressing enter to confirm converting religion in a province instead becomes an accepted DotF CTA or some similar nonsense. There's nothing to "be careful" about, the game trades you front pop-ups and if it happens at just the right time, you get screwed.
Putting new pop-ups last gives you the ability to avoid this nonsense, and also has the expiring events/pop-ups dealt with first. I don't know why the devs insist on new pop-ups on top, but so long as that remains the case any assertion to "be careful" is utterly invalid. No human being can react in under 100ms consistently (most of us can't break 200ms even when focusing, the average is higher), if you get hit by a pop-up while accepting another one within that timeframe while pressing enter you lose to fake difficulty.