If the US needed to use nuclear weapons on another country that isn’t China or Russia, do we tell them they’re not the target when we launch or before?

That is pretty much the standard procedure.

When one side attacks a third party, the other superpowers are always warned at least an hour in advance, that has been agreed upon a long time ago.

This gentlemen’s agreement includes the other superpowers not passing on the information to the country that is about to be attacked.

Maintaining stability has been the main focus of the military leadership since the Cuban Missile Crisis in all superpowers.