Order by & include array by specific post ids

use post__in key instead of include to get posts from the specific post ids.

$args = array(
    'post_type' => 'testimonials',
    'posts_per_page' => 4,
    'orderby' => 'ID', 
    'post__in' => array(883, 563, 568, 106),
); 

And to order posts by the given posts ids, you can use the following array.

$args = array(
       'post_type' => 'testimonials',
       'posts_per_page' => 4,
      'orderby' => 'post__in', 
      'post__in' => array(883, 563, 568, 106),
   );