You can use the -C option to run the command in the target base directory, or cd to that directory first. Include the full path to the tar files in the cat command.
If a file was backed up like 'home/<username>/file' then you can use something like:
cat /mnt/usbdrive/backupfile.tar.0* | gunzip | tar -C / -
The tar info file shows another example where the tar command that does the untarring is done in a subshell.
From the info manual:
Code:
For example, here is how you might copy a directory's contents from
one disk to another, while preserving the dates, modes, owners and
link-structure of all the files therein. In this case, the transfer
medium is a "pipe", which is one a Unix redirection mechanism:
$ (cd sourcedir; tar -cf - .) | (cd targetdir; tar -xf -)
You can avoid subshells by using `-C' option:
$ tar -C sourcedir -cf - . | tar -C targetdir -xf -
In your case, you are just unarchiving.
Looking at some of the contents of the archive will help determine where the current working directory should be.