Notify admin when Custom post meta data gets updated or deletet

Actually this is the right way of doing that and proper hook to work with in my opinion.
All you need to do is check if the updated meta key is the one you want to detect (that’s why there are 4 arguments passed to the hook!).

So let’s say your post meta is called 'email_triggering_meta':

function detect_post_meta_update($meta_id, $post_id, $meta_key, $meta_value) {

     // ignore every meta update apart from `email_triggering_meta` 
     if ( 'email_triggering_meta' !== $meta_key ) {
           return;
     }

     // code to email admin goes here
}
add_action( 'updated_post_meta', 'detect_post_meta_update', 10, 4 );