Custom post order returning posts from other categories

In WP_Query(), there is no category reference passed so this is the point which returns all category post.

Please try with passing category ID here:

$the_query = new WP_Query(array(
   'cat'=4, //Your category ID
   'posts_per_page' => -1,
   'meta_key'   => 'adult_price',
   'orderby'=> 'meta_value_num',
   'order'  => 'ASC'
 ));

OR

$the_query = new WP_Query(array(
   'category_name'=staff,   //Your category name...
   'posts_per_page' => -1,
   'meta_key'   => 'adult_price',
   'orderby'=> 'meta_value_num',
   'order'  => 'ASC'
 ));

Hope this would help you better.

Thanks!