As an interesting aside I recommend to the readers the "Lieber Code" of ~1863, put together by the legal scholar Francis Lieber at the request of Union authorities to codify laws of war. Do note there were two parts to just war theory, jus ad bellum (a just war) and jus in bello (justice in war - following legitimate laws of war).
Both the Red Cross and the Geneva Conventions were not in operation in the USA during the Civil War. The first convention leading to codification of relief for the wounded and such was held in 1863 in Europe - the Red Cross was adopted as the "neutral" symbol in honor of Henri Dunant the Swiss who started the movement for the relief of war wounded in the wake of the Battle of Solferino.
FWIW IMHO the winners always decide that their war was "just", history in the long run may or may not agree with them. This is not to say the CSA was "right" or "just", merely to say that the overall justice of a war is perhaps best judged by history. Having said that jus in bello, how a war is fought, whether "rules" are observed, can be determined relatively objectively. Of course this assumes that both sides agree that there are rules - for examples compare "rules" in nazis vs western allies as opposed to nazis vs USSR, or the war in the Pacific especially from the Japanese perspective.
Just my 2 pence