OK, I managed to solve it by myself… the main problem was, that I used the name of the custom post type instead of the name of the ACF-relationship-field.
$methods = get_posts(array(
'post_type' => 'page',
'meta_query' => array(
'key' => 'persons', // name of custom field
'value' => '"' . get_the_ID() . '"', // matches exaclty "123", not just 123. This prevents a match for "1234"
'compare' => 'LIKE'