Have you removed the previous primary domain's email accounts in CPanel's Mail section under Add/Remove accounts? If you haven't, I would do this. I would also remove and recreate in that area each of the email addresses in question so they are definitively associated with the new primary domain.
Hi Grace, yes I had removed the email account when I the new Primary domain took affect. The thing is that it was only one account then and just one account now, which is under the new Primary Domain.
The thing is that I don't and didn't want to set up an email account where the account name is the same as my Log-in name for cPanel. This is what is the default Primary Account name and can't be changed.
I'm Ok with that, but it shouldn't be sending the blank Autoresponders.
So, I'm not sure.