AquaMail does not do anything "special" for the Gear 2, it isn't even aware of it.
The Gear 2 is based on Samsung's own operating system (Tizen), and is limited just to Samsung's watches (unlike Android Wear which has watches from several manufacturers and so is supported by AquaMail).
What you're seeing is Samsung's software for the smart watch mirroring Aqua's status bar notifications (in the phone's status bar area), and messing up somehow. I'm can say that because, presumably, you're not seeing anything weird with Aqua's on-phone status bar notifications.
That the combination of:
- Samsung's own Email app
- running on a Samsung phone
- connected to Samsung's smart watch
operates together more smoothly -- really shouldn't be surprising, right?
Just in case the watch is mirroring Aqua's "ongoing notifications" ("Syncing mail in <account name>", "Push mail: <account name>" if you have those), not just "new message" notifications --
-- please check AquaMail settings -> look and feel -> turn off "Notification icon during sync and push".
But if that's not what it is, then you need to talk to Samsung (actually, it would be a good idea in any case).