How do I detect in which page ajax_query_attachments_args is loaded?

The answer is wp_get_referer(). This function is working inside ajax_query_attachments_args. I can then use get_post_type with the post id from url parameters

$referer = parse_url(wp_get_referer());
parse_str($referer['query'], $params);

if (isset($params['post'])){
    $post_type = get_post_type($params['post']);
} else if (strpos($referer['path'], 'post-new.php') !== false && !isset($params['post_type'])){
    $post_type="post";
} else {
    $post_type="";
}

if ( $post_type == 'post' ) {    
    $query['tax_query'] = array(
      array(
          'taxonomy' => 'category',
          'operator' => 'NOT EXISTS'
      ),
    ); 
}