On the whole the Ice Age was getting colder and colder, and it was probably relatively easy to walk back to North Africa since sea level was about 400 feet lower. So if I were in freezing Europe, I might have wanted to migrate back to Africa.
I suspect there was a lot less water in the Mediterranean during the Ice Age than we realize. A whole lot less.
There are scowering marks in the bottom at the Atlantic entry point at Gibralter. I suspect there was a plug at Gibralter that broke as the Ice Age melt raised the water level in the Atlantic.
After the Med was filled, the 'plug' at Bosporus broke and the fresh water Black Sea was flooded.
There was enough flooding going on that there must be legends everywhere about floods.