After a restart the system still boot's from that external backup even if the "system-folder" is not in root and therefore in a directory that is called like the original harddisk. so "Macintosh HD / System folder".
The System Folder can be anywhere on the disc and can be named anything. If it's got the icon with the little Mac inside, it'll be working. To stop it working, drag the System and/or Finder out of the folder and verify that the icon has changed to a normal folder icon.

