My wife forgot the password to her Apple ID account. Her Macbook Air (OS X Yosemite) restarted to install some updates. She has her user account set up through her Apple ID account.
Since she forgot the password she reset it from my laptop.
She can log in to iCloud and Apple ID with the new password, but cannot log in with the new password on the Air.
When she tries to log in she is greeted with this message:
"This account uses an iCloud password to log in. If you need to change
the password, use another device to change it at appleid.apple.com."
Best Answer
To anyone still needing help, this is what was done to fix this issue.
If you reset your iCloud email and password online that does not update your icloud account on your computer with the new email address.
You need to login to your iCloud account online and set your primary email back to the original one (your computer is still using this email) reset the password if you would like.
Now restart your computer and you should be able to log back in.
Once you are logged in, go back to iCloud website and change back to your new email.
Before you log off your computer go to Setting>iCloud and remove the old iCloud account and add the new iCloud account.
That should be all you need to do.
Now your computer is using the new email and you should be able to login using your new password.