1. USERS GET THE PUSH NOTIFICATIONS BUT NOT THE EMAILS
Shopney is taking care of the mobile push notification side of this operation. If the push notifications are being delivered properly, the issue is most likely about the Back In Stock side. You should contact their support.
2. USERS CANNOT GET THE RESTOCK PUSH NOTIFICATIONS
This case never happened so far. But if it happens, we need to check your store and its settings specifically. Please contact Shopney support team.
PS: At Shopney, we work hard to make all of your favorite apps get functional also in your mobile stores. Please feel free to check 'integrations' section of your Shopney dashboard to see what more we offer as integration.