I had a similar problem.
I was setting up my HomeKit for the first time. Everything was running smooth until I tried to add my wife to created home. I kept getting an error that said: "Invitation Failed - Could not invite "username@icloud.com" because the email address is not registered with iCloud."
I knew for fact that it was. So I did a google search to find an answer.
I tried a few but they didn't seem to work.
Tried restarting the phones.
tried adding other people which seemed to work just fine but I couldn't add my wife.
Apple phone support had me log out of her iCloud account and back in but it didn't help.
What finally did help for me was this.
I went into my wife's iPhone and sent an invitation to my iPhone. That worked without a problem. Then I sent her an invitation again from my iPhone and it registered and it has been working perfect since that point.
So I'm not sure if that was the solution or just a clitch. But if you are having troubles with this maybe give that a try.
Cheers!