Like I said it worked on my Note 5 with a notification for each email, just like you described on my Gear S2. On my new S7 Edge with the new marshmallow tho, it's just one notification mirrored onto the watch with the same exact settings.
Oh it did, sorry missed it.
Did you have Android Wear app or Pebble app installed?
When the app sees those, it "enhances" its notifications for the Wear.
If yes, please try installing one of those two apps (and just run it once, nothing else), and if it helps, please let me know -- it would mean that Samsung's software for this smart watch can emulate Android Wear, so I'll want the app to make use of it.
If you never had Android Wear or Pebble app installed on the old phone, then -- well, what can I say? -- you had X working on Samsung Y and then X doesn't work on Samsung Z, even though the app is the same, and the difference is Samsung device Y vs. Samsung device Y.
If I were you, I'd be asking Samsung about why with Z it's different than with Y.
As for me, given that the app isn't aware of Tizen watches, I can't even imagine how it could have possibly worked on the old phone.
The only possibility I can imagine is if you had Android Wear app or Pebble app installed too, and so Aqua's notifications were "Android Wear enriched" and mirrored like that, as individual "cards" to the Tizen watch.