The War of the Magi was separate from the the war of the Warring Triad. During the War of the Magi, Espers already had free will, and there was a known time of peace between Espers and humans before the War of the Magi, so the Warring Traid must have already been out of the picture by the time the War of the Magi rolled around. The timeline of the FFVI world goes something like this:

The Warring Triad is banished to the mortal realm. They begin quarreling with each other, and create Espers from humans to fight for them as living weapons.

The Warring Triad realizes they are being mocked/pitied by the other "gods" that banished them here, and stop fighting. They turn themselves to stone and give Espers their free will.

A time of peace follows between humans and Espers.

Humans eventually figure out the secrets of magicite and begin using Espers to gain magical powers for themselves. The War of the Magi eventually breaks out, and humans, Espers, and mages are involved on all sides.

The War of the Magi ends, Espers leave the mortal world for their own world and take the statues of the Warring Triad with them. The remaining mages are hunted down, and the survivors hide themselves away in Thamasa.

Without mages, Espers or the Warring Triad, magic ceases to be a major force in the world, and is forgotten.

Nothing happens for a long time. The Dark Ages.

Technology is rediscovered, and civilization begins to recover.

Empire seeks out Esper magic once again, and threatens to repeat the War of the Magi.