As part of a propaganda campaign, the US did drop leaflets on many cities that said, in essence, "we're going to be destroying lots of cities, including maybe this one, so flee your jobs ASAP." One should not mistake this with genuine care for civilian lives — it was acknowledged even at the time to be a psychological warfare campaign, meant to encourage absenteeism.

The US, as an aside, did not warn the Japanese about the atomic bombs, though sometimes you see rumors to this effect on the Internet. I have written up a discussion of this at length, here.