Do military officers ever REALLY have to say "tHat's aN oRder!" like they do in fiction?

No. I was in the US army for five years. I never heard any NCO or officer say, “That’s an order” a single time, not even jokingly.

It would/does sound both redundant and pointless to anyone in the military. If someone senior to you tells you to do something it’s already an order. Saying “That’s an order” just sounds weak.