After you have hit Cmd + Shift + c (go to computer) you can browse to :
name_of_computer/name_of_disk/Users/toni, and see if the OS X default folders are here or not.
Example :
Toni's iMac/Macintosh HD/Users/toni/default_folder_here.
If toni's account only has Applications, Conduit, Desktop, Documents, then something when wrong in this account and you won't find the Library.
TM backups ALL by default, unless you exclude some specific folder/file.
name_of_computer/name_of_disk/Users/toni, and see if the OS X default folders are here or not.
Example :
Toni's iMac/Macintosh HD/Users/toni/default_folder_here.
If toni's account only has Applications, Conduit, Desktop, Documents, then something when wrong in this account and you won't find the Library.
TM backups ALL by default, unless you exclude some specific folder/file.