During an Ice Age, the world's water DOES accumulate as ice at the poles, lowering sea levels. When the planet heats up again, the stored ice melts back into the ocean, raising sea levels again. That's exactly how it works.
AI would have us believe that sea levels rose a hundred or more feet - presumably due to ice melt, because where else could the water come from? And then a millenium later the earth froze... but somehow the water didn't recede again.
This would only happen if the whole world froze at once, a la Day After Tomorrow. Which is theoretically possible for a few reasons - supervolcano eruption, meteor or comet impact, nuclear winter - some sort of disaster that covers the whole planet in heavy cloud or dust, blocking all sunlight and creating freezing temperatures across the entire planet simultaneously.
Although it's possible the movie had that in mind, it doesn't mention it.
So at face value the movie seems to be saying "Earth warmed up, sea levels rose. Earth cooled down, sea levels stayed the same". Which suggests they didn't quite think their clever scheme all the way through.
Unless the movie is suggesting Manhattan sank INTO the sea, which is also rather a silly idea.