If I open an external drive, or an folder on that drive, in the Finder, then enter Time Machine by clicking on the menu bar icon and selecting "Enter Time Machine", then Time Machine runs, but it jumps me back to my User folder, rather than using the currently open folder that I have opened up on my external drive.
This problem does not occur if I enter Time Machine on my internal drive. Does anyone else have this problem? I think it started happening recently, perhaps after I upgraded to Mavericks.