I have played 2 games with the Tower, and in both cases, only the winner received any points from the tower, despite both players having cards from the empty piles.
Do you have the game number for that game? It is is a known bug (http://forum.shuffleit.nl/index.php?topic=1611 http://forum.shuffleit.nl/index.php?topic=1348) that the end screen will not (or only partially) list the points for Tower in the detailed overview, but will apply them in the upper part where just the score is listed.