Q: iCloud Events Invitations

I currently have an iPhone 6 and a MacBook Pro Mid-2015. I didn't have this problem before; it was not until recently that I realized I was having trouble receiving event invitations in my current iCloud Calendars set up. My calendar events invitations do not pop up anywhere but in my Gmail. I thought iCloud calendar takes over the Gmail calendar invites? I used to get those notifications within my Calendar apps both on my phone and computer.

My main email is gmail so my current Apple ID login is used with my gmail. When people send me invites to events like to (___@gmail.com). I do not get notifications on my Calendars apps on iPhone or Mac. I could send out invitations easily myself. But I cannot get any in-app notifications to RSVP to events in both the iPhone and Mac versions of the Calendar App. I have checked via http://icloud.com of my calendar preferences and it shows that I opted to "Receive event notifications as in-app notifications". So whenever people send me invites, I have to visit the Google Calendar webpage to see the event. I do get emails of the invites, but they are all sent from my Google account. I thought iCloud could take care of the invites? It's really frustrating and I do not know what to do.

Is it because the people sending me notifications are sending invites via the Google Calendar Webpage? Is there some setting I am missing? Should I call Apple Support or visit the Genius Bar? Please let me know what I should do because I rely on iCloud Calendar for personal and work.