You need to create taxonomies specific to your post type using register_taxonomy
instead of using the taxonomies argument when registering the post type.
http://codex.wordpress.org/Function_Reference/register_taxonomy
// categories
register_taxonomy(
'project_categories',
'projects',
array(
'label' => __( 'Categories' ),
'rewrite' => false,
'hierarchical' => true,
'capabilities' => array( 'edit_terms' => 'manage_categories' )
)
);
// tags
register_taxonomy(
'project_tags',
'projects',
array(
'label' => __( 'Tags' ),
'rewrite' => false,
'hierarchical' => false,
'capabilities' => array( 'edit_terms' => 'manage_categories' )
)
);