This is just my guess, but it's possible Adamantoise isn't on the same 'data center group' as Odin is. Hence the character selection screen will only show the servers attached to that currently selected data center. To change the data center, on the main title screen, click 'Data Center', and then scroll through the list of Data Centers until you find the one that has your desired server on it (in your case, your server is Adamantoise).

I can't remember off the top of my head right now what Data Center group Adamantoise is on sadly but you should be able to find it without too much trouble by the above method. Then once you select that Data Center, the client will memorize it and from then on will only show servers attached to that specific Data Center. Hopefully that wasn't too confusing.

EDIT: Nekodar stated it. Thank you for that.