The site admin will not receive an email notification when they have manually created a Member. This is because the site admin created the member account so they typically don't require an email notification for that.
There is an option to send the Member the New Member Notification email when a site admin manually creates a Member.
The site admin can check the “Send New Member Notification” setting when adding a new member manually and the Member will be sent the email.
So that box can be checked to send the New Member Email Notification to the member. If checked, the email will be sent to the member when the blue Add Member button is clicked.