It rather looks to me as tho' you're writing before there's anything there i.e.

$tar->write('Test2.tbz', COMPRESS_BZIP);
$tar->add_files(@files);
[download]

should be

$tar->add_files(@files);
$tar->write('Test2.tbz', COMPRESS_BZIP);
[download]

Referring to Archive::Tar, we see that add_files() only adds files to the in-memory object i.e. not to any file that may have been written using write() ... unless, of course, it's nealry beer o'clock on Friday afternoon and I've missed something even more elementary :-)