Where did Chat and Max end up?
At the end of the story, Chat, along with Reid Hershel and Farah Oersted, prepare to travel to Celestia to visit Keele Zeibel and Meredy.


Taken from Aselia Wikia

So, it seems to me, that Chat ended up on Celestia, even if it was only for a temporary visit.


  But after his perceived victory against Balir, Max asserts himself as the de facto ruler of Celestia


Taken from Aselia Wikia

Which makes me think, that he would also end up in Celestia. Especially, since it seems his wife wanted to join him again:


  At Jini, the artist tells Reid that she completed her sketchbook and that she can finally offer it to the sea to the childhood friend of her memories. By doing so, she says she can now return to her husband to resume their lives together, revealing herself to be Max's wife, Lesitia. 


Also taken from Aselia Wikia