Ok, sounds like two things here:
1 - There being only one notification icon, even though there should be two. What is this single icon? A notification for one of the accounts? Always the same one, or different at different times?
2 - The icon clearing on the tablet -- normal, since in two panel layout, when you launch the app, it has to open some folder (in the right pane), and picks the first account with unread messages (in the left pane). This counts as "opening" that account, and clears its notification.
I'm not sure what's going on with number 1 though.
Even though you haven't cleared any settings yourself, can you check them - on the phone - since it's the strange of the two?
Specifically, how about checking both accounts' "special settings" (long press in the account list), to see if you have an override of app global settings, and that override has notifications turned off?
I'm posting a screenshot.
The first checkbox ("on"), "Special settings", tells Aqua that you want this account to have notification settings that are different from the app's global settings ("special").
The second checkbox ("off"), "Enable notifications", tells Aqua that you want this account to not post notifications, as part of this "specialness".
I'd recommend turning off the top checkbox, telling Aqua that you want this account to use the app's global settings for notifications, not special per-account settings. Maybe just do it as a test.