Custom Taxonomy – Tags Metabox is showing instead of Categories

You need to set hierarchical argument of your taxonomy to true (by default it’s false):

function product_category_taxonomy() {
$labels = array(
        'name'              => __( 'Product Categories' ),
        'singular_name'     => __( 'Product Category' ),
        'search_items'      => __( 'Search Product Categories' ),
        'all_items'         => __( 'All Product Categories' ),
        'parent_item'       => __( 'Parent Product Category' ),
        'parent_item_colon' => __( 'Parent Product Category:' ),
        'edit_item'         => __( 'Edit Product Category' ), 
        'update_item'       => __( 'Update Product Category' ),
        'add_new_item'      => __( 'Add New Product Category' ),
        'new_item_name'     => __( 'New Product Category' ),
        'menu_name'         => __( 'Product Categories' ),
    ); 
    $args = array(
        'labels'            => $labels,
        'public'            =>  true,
        'show_in_nav_menus' =>  false,
        'has_archive'       =>  true,
        'hierarchical'      =>  true,
        'rewrite'           =>  array('slug' => '/products', 'with_front' => true),
    );
    register_taxonomy( 'protax', 'product', $args );
}
add_action( 'init', 'product_category_taxonomy');

Take a look at codex documentation.