Today, having connected phone to my new Gear S3, I have the problem. So I guess it is the way the S3 is handling notifications (differently to S2). I understand this is beyond the control of the AquaMail App ... but reporting it anyway.
Please check Aqua Mail settings -> message notifications -> make sure that "smart watch enhancements" is enabled.
If that item isn't there please make sure to install Samsung official Gear app.
Re: With other mail Apps (Blackberry Hub) the notifications come through OK.
Some apps may have support for Samsung's Tizen based watches specifically.
Aqua Mail only supports Android Wear. The Samsung Gear app is then responsible of "translating" Wear enhancements for the Gear watches.