Is the app checking mail in this account?
If not, that's the number one issue to solve (calendar sync is triggered every time the app checks mail).
Assuming it does, does doing Menu -> Refresh (Menu -> Sync, etc) in your calendar app brings things up to date?
If you go into system settings -> accounts, and click into the Exchange account ("owned by" AquaMail) -- is there Calendar item there? Does it have "sync enabled"?