I haven't seen anything that addresses this problem, so hopefully there's a solution:
I have an iPhone 5 with iOS 7 installed.
I use Gmail for all my email addresses, I have multiple accounts that I access via my phone. The two most important are a personal Gmail and a work email.
The work email is Gmail also, but I have it mapped to a domain that is used for work. (e.g. so I can send from @mydomain.com instead of @gmail.com).
I received an iCloud invite from someone, and the first time, it entered into my calendar on my iPhone (I use the Apple Calendar app). The invite got updated, but my calendar invite did not update. I saw it in my "replied" list under the "inbox" button on the bottom right of the app. I was able to decline it and it disappeared off my calendar, but it did not update.
I tried doing a test invitation from my personal to my work email, and while I can accept the invite (using the iCloud accept / maybe / decline butons), it still doesn't show up on my calendar on my iPhone or Mac.
How can I get these to work?
I figured out this only happens when you use a special setup.
Apple doesn't send the event as an email, it is only displayed as a calendar notification.
How to solve
Robin // https://twitter.com/_RobM
I called Apple support and they checked a few things on my mac:
The problem was solved, and I started receiving notifications in the iCal app right away, and no more annoying e-mails with .ics attachment.
I checked Safari in the iCloud settings and still working fine.
Hope this helps