The "start the app in" only applies if you've completely closed the app with the Back key.
Pressing Home, by convention, preserves the app's state, you can think of it as "minimize" in Windows. Android will keep this saved state for up to 30 minutes.
Next.. you mention "widget"... AquaMail's widgets, by design, "point to" some "location" in the app -- such as a specific folder, an account, or the account list. Launching the app from a widget will take you to where that widget "points to".
Finally, if any accounts has a login error, then Aqua will start in the account list, so the user can see the error ("hmm, why aren't there any new messages").