For mobile push notifications, if a member has a phone that is green to the left of their name, then they should be receiving those notifications.
If the phone does not appear, then the user either does not have mobile notifications turned on or they could have uninstalled the app/never installed the app and registered from a Membership/Event/Trial/Retail url.
To trouble shoot this and make sure the user can receive in-app mobile messages. Please suggest the user sign out of the app, delete and reinstall the app on their phone. Make sure they click to "Allow" notifications when first loading the app. This should reset their notifications settings. If any issues persist please reach back to our customer support so we can trouble shoot further.