I've recently switch to iCloud Calendar (and Contacts) from Google. My primary Apple ID (and email address) is still my Gmail address, my secondary is @me.com, and my alternate is @icloud.com. Calendar invites sent to any of the addresses from Outlook or Hotmail arrive as emails and an ICS file attached. They do not pop up as alerts. Updates to the events also arrive by email and even tapping the ICS file does not update the name/time, etc. (or whatever was changed) as intended. Yet, if sent an invite from iCloud to my work Exchange address, I get the in-app notification and it's automatically added to my calendar. I assumed this behaviour was supposed to work both ways when an ICS file was attached. Is there a trick to getting this working that I am missing? I have checked the "In-app alerts" setting in iCloud and it is configured correctly.