Bought my wife a Vivoactive 3 primarily so she could get notifications on her wrist. Everything works but Messenger: texts, emails, Facebook notifications all work. We spent our entire Christmas trying to get this to work, and everything seems to be set up the way it should be. Droid Turbo 2 running Android 7.0.
I just switched from iOS to Android and noticed this. There is a difference on Android (for me at least with 8.1) where you have to whitelist EVERY application you want to have notifications show for on the watch. This is in Settings -> Smart Notifications (in Garmin connect app). Click the overflow button at top right and add the application you want to get watch notifications for. It's rather annoying, this isn't an option on iOS and it just works, however there are more features on Android like responding to messages from the watch.