This was emphatically not the anti-matter universe, nor was it supposed to be evil. That was the ridiculous story that the most overrated writer came up with many years later in JLA: Earth-2. This was the pre-Crisis Earth-3, wherein the identities of the heroes and villains were reversed, but good was still good and evil was still evil. People had the free will to choose, and good could triumph over evil.
It was the case that certain historical events were inverted in certain ways, so that, for instance, the US conquered Britain at the end of the 18th century, etc. But the CSA beat the JLA on Earth-3 not because Earth-3 favored evil, but because it favored its natives.