Well, not quite. There were three sides, one of which we only recently even found out about. White Mages of Amdapor were on one side, yes, but Black Magic is a later development. The Void Mages of Mhach are specifically stated to be on the vaguely defined winning side. Also, there were the Scholars of Nym.

We only just found out a bunch of stuff on the Mhachi, so bear with me. We know that the Nymians were taken out by a mysterious virus that turned them into Tonberries. Recently, however we found out that the disease was caused by a voidsent servant of the Mhachi. This has lead to some thoughts that Diabolos may also be one the Mhachi's machinations (a... Mhachi-nation, if you would), which could only be kept sealed by the White Mages, who had to draw upon a great amount of power from the Elementals, which in turn caused the Sixth Umbral Calamity.