If it is supposed to work with ACF I would contact them and ask why it’s not working with ACF local JSON feature. This feature was not available in ACF4 and ACF5 was just recently released as a free version. Maybe that’s the problem. I can’t say. But if this plugin needs to be used and you need to sync the fields on all sites then there isn’t an automatic way of doing this or causing ACF to do it.
