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!