Please check out in phpMyAdmin the table smf_log_notify (replace "smf_" with your actual database tables prefix): you will see there a way to map ID_MEMBER to an ID_BOARD and respectively to an ID_TOPIC.
I think the line you need to insert (to register the member for notification on a particular board) would be like:
INSERT INTO smf_log_notify (ID_MEMBER, ID_BOARD) VALUES (new_id_member, id_board);
where "smf_" should be your database tables prefix, new_id_member should be the ID_MEMBER of the last member in the smf_members table (that is, after the new member was registered), and id_board should be the id of the board you want the member to be notified about.
Alternative: since users are manually registered by an admin, you might be able to make it a little easier: typically in the case of your forum, I would suppose each user is registered one by one so there are really little chances (if any) to have two users registered in the same minute.
If that is the case, you could count on the fact that the last registered member is still the same until you go and edit the database, so you could use MySQL to get itself the last ID inserted in the members table, and have it inserted directly:
INSERT INTO smf_log_notify (ID_MEMBER, ID_BOARD) VALUES ((SELECT max(ID_MEMBER) FROM smf_members), id_board);
You still need to replace manually id_board with the proper id of your board.
Note that in case another admin registers another member meanwhile, meaning after you (or anyone) register a member, but before you manage to execute this alternative code, then the notification will be set up only for the last member, you might miss the previous one.