As nearly as I can discover the palm out salute is correct for the American Civil war era. But, at least some of the time, only the highest ranking soldier in a group would salute the approaching officer. Everyone else in the group would come to attention until released by the officer. With the Civil war it can be kind of a crapshoot as to accuracy. There were units specifically raised by the US Army but there were also units raised by state militias and or raised /equipped by private groups. These militias and private units may or may not have been trained or even uniformed to the same standard as units equipped by the Army. As the war ground on things became more standardized. As for anything coming out of Hollywood, drama trumps accuracy every time.