Correct if I'm wrong. I'm new to the lore forum so I keep making some mistakes, but the Allagan empire fell one or two umbral eras before the War of the Magi. Like Wyrah said, you just mixed up the two thing.
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yes it is suspected the 3rd was allagan fall and war of magi was 5th umbral
Allag ended with the Fourth Umbral Era. The War of the Magi triggered the Sixth Umbral Era.