By design, an iPhone will sync or manually manage iTunes content with one computer at a time. Any attempt to sync or manually manage with a second computer will result in all iTunes content being first erased from your phone, to be replaced with the content from the second computer. This is a design feature of all iPhones and cannot be overridden. Been like this since the first iPhone was released.
"Your phone is Synced with another iTunes Library do you want to erase this iphone and sync with this itunes libary".
As the message infers, you can only sync your iDevice to
a single iTunes library. The only way around this, which is
of no real use to you now but for future reference, is to have
your iTunes library (entire iTunes folder) an a separate hard
drive and carry it around where ever you go. Any computer
you have will need to be set up to connect its iTunes to that
The one caveat of this is that is backups of the iDevice.
Each computer will have a different backup file depending on
when you synced to the computers (backups are stored
in ~/Library/Application Support/Mobile Sync/ Backup on
the computer not in iTunes library). Where this is problematic
is if you need to do a restore and you only have a computer
available with an old backup and not the most recent.
The other problem will be if you manage Address Book, Calendars,
etc. different on different computers. Things can get jumbled, lost,
or just plain add duplicates.
As for your current situation, there really isn't much you can do.
the iphone only can be sync to one computer only
eventhough the manually manage has been checked according HT1202
Yes, apple has lied to us. See https://discussions.apple.com/thread/4040459
Use 3rd party software like Copytrans manager free on others computer for controlling your iphone library. but it need itunes driver.