WP_Query with multiple orderby NOT working with ASC and DESC, what’s wrong?

Your code is invalid (syntax error, missing closing array and semi-colon), and incorrectly nested – if you were to properly indent your code, you’d have something like:

$args = array(              
    'tag' => 'tag-AAA,tag-BBB',     
    array (
        'orderby' => array(
            'title' => 'ASC',
            'post_date' => 'DESC',
        )
    ),
);

See how orderby isn’t actually a property of $args? You need:

$args = array(              
    'tag'     => 'tag-AAA,tag-BBB', 
    'orderby' =>  array(
        'post_date' => 'DESC',
        'title'     => 'ASC',
    ),
);

I’ve also switched the order so that posts are ordered first by date, then by title.