When MyHeritage sends an e-mail inviting a family member (either because an e-mail was added or user clicked on "Invite more members") the e-mail displays as coming from MyHeritage Invitation. Many recipients don't know who that is and just delete the e-mail as SPAM.
I suggest you have the "From:" changed to the e-mail address of the member that was logged on. They will recognize that name right away.