This is not a bug. This is the Desktop App behaving as expected. If you have different Battle.net accounts for different regions you will need to be signing out and switching between them, as well as making sure you are signed in to the correct region for the account you are using. Additionally when running a shortcut from the desktop for a game the expected behavior is that the Desktop App will launch with the indicated game's tab in focus, allowing you to press Play and launch the game.
Make sure you are also using the drop down above the Play button to launch your game into the correct account and region for the currently logged in Battle.net account.