Those were different times, but on the most part those Greeks who came from Asia Minor were not treated well by the locals.
The Greeks of Asia Minor were industrious, hard working people. Most of them merchants and business owners for several generations. As mentioned above, these were people who were not afraid to move and migrate in times where travelling just a few kms from village to village was considered a huge undertaking. As compared to the Greeks of the mainland they were much more "cosmopolitan" living in much more open and diverse societies.
It's no surprise that people like myself and ajax chose to migrate again, just a generation or two after our ancestors moved back to mainland Greece. Moving around is probably in our genes
It's unfortunate that there are most likely no records showing all these migrations, but one can imagine those enterprising ancestors moving from place to place every few generations. Sometimes driven out by conflict, or sometimes by the need to find a better place to raise their family, and yet other times by a sense of adventure. Those were no easy trips and easy moves by any means. I can imagine my ancestors moving from Crete (or possibly some other island, Chios possibly) to Aivali back in the early 1800's. Loading a small boat with all their belongings and heading to a land just recently vacated because of the massacre of the local Greek population. I can imagine how daring these people must have been. And then the grandchildren of these enterprising people had to move again a century later, back to Greece proper, again because of persecution by the Turks. And then roughly another century later these people's grandchildren (ajax and I) had to move again - for different reasons this time - further away from our ancestral lands.
Ajax sees himself a person without a country. My country, my home, is the Aegean sea. This is where most of my ancestors lived and died. Be it Crete, Chios, Aivali, Smyrna, Constantinople or Piraeus, they spent their lives in or around the Aegean sea. That's my home, and it really feels like home every time I go back and I look at my beloved Aegean sea.