New members do not automatically have any alerts, you will need to set these up for your new member if you do not think they will do this themselves.
You set up an alert for another member the same way you would for yourself. Once you have defined the scope of the alert using the search function, you choose Create alert but type the name of the person you wish to set it up for, then click Save for member
You can set up a digest for them in the same way.