When you have Microsoft Outlook 2016 or Outlook 2013 running as a RemoteApp in Windows Server 2012, you don't receive new email desktop alerts (toast notifications) as expected.
New email desktop alerts are created by explorer.exe. In a RemoteApp session, explorer.exe does not exist. Therefore, it can't create alerts.
Microsoft has confirmed that this is a problem in Outlook when it's running as a RemoteApp in Windows Server 2012.