Yes, knowing if that "bad" account's notifications are posted to the phone's status bar would help.
That's "step 1", Android Wear notifications are just enhancements "attached" to the "good old" status bar notifications.
Other than that, Aqua will only notify about *unread* messages, and each account's "stream of cards" on the watch is separate (so you should expect to see all the cards from one account and then all the cards from the other).