I think what you’re trying to do here is create a custom hook. You should just do this to make it work correctly:
<?php if ( is_user_logged_in() )
my_redirect(); ?>
There’s no need to make it an action if you can use the function directly in your template. Actions are primarily used when you want to alter the behavior of core or you don’t want to alter an already existing template.
Since you’re creating your own template anyway, just call the function directly to reduce overhead. I would do this before get_header() or any characters are rendered or you will receive a PHP error.