Adding action to save_post, post needs to be saved twice for function to work

This is a stab in the dark, but have you tried using the set_object_terms hook for your bam_save_event_cat function?

function bam_save_event_cat( $post_id, $terms, $tt_ids, $taxonomy, $append, $old_tt_ids ) {
    $taxonomy = 'categoria';

    $tribe_cats = get_the_terms( $post_id, 'tribe_events_cat');

    foreach($tribe_cats as $tribe_cat) {
        if( empty($tribe_cat->name) ) continue;
        $catname = $tribe_cat->name;
        $cats[] = $catname;
    }
    wp_set_object_terms( $post_id, $cats, $taxonomy );
}

function bam_save_event($post_id) {
    if ( defined( 'DOING_AUTOSAVE' ) && DOING_AUTOSAVE )
        return;

    if ( !current_user_can( 'edit_post', $post_id ) )
        return;

    if(get_post_type( $post_id ) == 'tribe_events' ) {
        remove_action( 'save_post', 'bam_save_event' );
        wp_update_post( array( 'ID' => $post_id ) );
        add_action( 'save_post', 'bam_save_event' );

        add_action( 'set_object_terms', 'bam_save_event_cat', 10, 6 );
    }
}

add_action( 'save_post', 'bam_save_event' );