That depends on what the other plugin is expecting to see in the custom field. An ACF relationship field stores an array of Post IDs. In the DB this is stored as serialized data.
When you do a reverse relationship query, which is what you need to do in PHP to get all the users associated with a post you need to do a LIKE query on the value "{$post_id}" (note the “s). So the plugin needs to be able to look for values that are “LIKE” the value you are looking for rather than exactly equal to.
