In the info file, the tpl is loaded as:
files = theme/jplayer.tpl.php
The jplayer.tpl.php file, however, is located in the root directory of the module, not in the "theme/" directory.
Per the Drupal 7 module development documentation (http://drupal.org/node/542202):
"all modules must now declare any code files containing class or interface declarations in the .info file"
Apparently the current situation is not breaking anything, but I'd prefer if it were clean.
Attaching patch in a sec'