Categories and tags for custom post types

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' )
  )
);