Orderby modified only for specific post types

Am Afraid that you have to go with Direct MYSQL or you can run two WP_Query() and then combine them, sort them or sort them with WP_Query() then combine them.

Here is an example

$args = array(
  'post_type'      => array( 'staff-updates', 'coreteam',
                           'developing-updates', 'vacancies', 'recognition', 'page' ),
  'orderby'        => 'modified',
  'posts_per_page' => '10',
  'order'          => 'DESC',
);
$the_query_modified = new WP_Query( $args );

$args = array(
  'post_type'      => 'employees',
  'orderby'        => 'date', //default to post_date
  'posts_per_page' => '10',
  'order'          => 'DESC',
);
$the_query_published = new WP_Query( $args );

$combined = new WP_Query();
//combining two to one
$combined->posts = array_merge( $the_query_modified->posts, $the_query_published->posts );

Now $combined->posts will have both. Then do whatever you want. $combined might miss few details since it is not direct constructed. In that case you just manipuldate with two queryies( $the_query_modified,$the_query_published ) directly or go for SQL

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