"Once you assign applicants to a private application in the Application Invitation, an email will automatically be sent to those applicants. (Notification Center> Email template Name>Application: Application Invitation).
If you do not want this email sent you can turn this feature off in the Administration Dashboard - Site Settings - General Settings - Disable Automatic Notification for Application Invitation.
If you turn this feature off, you must also select "Yes" on the option in Site Settings -General Settings - Enable Automatic Application Creation through Application Invitation."