Whether the Allies cared much or not is also moot in terms of what they should've done, morally speaking. Clearly my opinion is they didn't care enough. Clearly I find the firebombings morally disgraceful as well. Clearly, at least some people involved in the decision cared a little, as several people did lobby for a demonstration. The US also was known to airdrop pamphlets encouraging civilian evacuation of cities; civilians weren't a total non-concern.
It's not anything like North Korea threatening the US with a space laser. For a multitude of reasons: US spy capability means they would know well in advance the details of any North Korean space laser. North Korea isn't an alliance of the most powerful nations in the world with leading scientific and military capability. And if North Korea did indeed demonstrate a space laser that could obliterate a city in a fraction of a second, you'd better believe the US would stand up and take notice, for that matter.
Moreover, at the time an atomic bomb wasn't science fiction. Everyone at that point had known that an atomic bomb was possible for decades; both the Germans and the Japanese were trying to develop one. Given that, if the Americans said, "we've succeeded in developing one and intend to use it to destroy your cities unless you surrender", along with a demonstration of in action, it wouldn't be unthinkable that the Japanese would take it seriously - nor would it be particularly different from the Potsdam Declaration, which demanded surrender lest they face "utter destruction" without any specifics, which the Allies did indeed think was worth saying.
Delivering a reel of film would have been straightforward; even in total war all communication channels aren't cut off. If you want to do a real-world demonstration that can be observed, find a place to detonate it where it will be observed but will do minimal damage. The Manhattan Project involved solving many, many problems; this is just another one, and a relatively small one at that. When confronted with a problem, you figure it out.