The villagers of Thamassa are (SPOILER) descendants of the humans who used the powers drained from Espers and fought against them.

The War was precipitated by a (SPOILER) conflict between the three goddesses. Some humans got caught in the cross fire and were turned into Espers.

There's not much to add because the details about the War are very sketchy.

However here are some reasonable assumptions:

1) Many of the present Espers were most likely alive 1000 years ago (they may age differently). It's doubtful that humans alive at the the time would still be in the present.

2) The 8 dragons, Phunbaba, and Doomgaze were involved and got sealed sometime during the War.

3) Some of current cities in FFVI may have existed 1000 years ago. Tzen is a good candidate.