[1]https://noc.ac.uk/news/global-sea-level-rise-end-last-ice-ag...
I guess we may have to live with guesswork as I doubt we'll have convincing answers.
People could not just move inland; other people already lived there. Australians still keep careful oral records of negotiated resolutions of conflicts over living space when Sahel, between Australia and New Guinea, was inundated.
Between where Indonesian islands are now, and for hundreds of miles off the coast of Viet Nam all the way to Korea, were millions of square miles of prime habitat ("Sundaland"), also for tens of thousands of years. Every tribe there had to find somewhere else to live.
We can't presume people lived "there" if we don't know much of the above.
Nomadic people have very rarely ranged over more than a few hundred miles. We have here thousands of miles. There is room for every variation you can imagine, and even more you can't.
Rather, there was.
I harbor doubts about their receptivity to the correction.
This is exactly what happened in the British Isles when low lying Doggerland (between modern England and Denmark) was wiped out by a wave which was likely caused by an underwater landslide; that wave was in turn caused by the melting ice at the end of the ice age, which was otherwise causing gradual sea level increase.
They probably flooded increasingly regularly before being abandoned and eventually subsumed, no unlike Venice today. Some could have been much quicker though, there are fault lines through the region though, so it's entirely possible a small tsunamis could have knocked out villages that sea level rise made vulnerable.