Hi Gail,
When I login into MyAppleID on the PC it shows both my primary and secondary email addresses, neither of which is the old @me.com account. That was going via System Tray->iCloud->manage ID,
On the Mac - System Preferences->Internet Accounts shows the correct iCloud account.
On the 6+:
Settings->iCloud - correct account
Settings->iTunes - ok
Seting->Mail - ahhh the old @me.com is listed there and the icloud account.
I have now Signed Out, and removed it from the 6+
I isn't on the Air2.
So far no error message or dialog box requesting the @me.com password.
All other functionality seems ok.
Cheers
Kingsley