This. I had enabled everything except notification access for ATN Manager in settings.
Go to Settings > Security > Notification Access and check the box beside ATN manager.
On a side note, does anyone have a way to get apps made for Gear 2 Neo on Samsung Apps store on Nexus 5? These default apps are okay but dont really do much in long term use.
In Gear Manager go to Notification and uncheck "Limit notification" and "Keep screen off" but do enable "Preview message"
There should be a section in there called "1) Instant alerts for Gear)" you should see "incoming call" underneath it - enable it.
After this, there should be another section underneath the first one "1)Notification for Gear apps", you will see ATN Manager in it - enable that. and below all of this should be "9) More notification". Select apps you want notifications from, for texting I use a third party app called EvolveSMS so therefore I had to enable notification for that app instead of Hangouts.