When you installed it did it give you an option to install for one or all users?
Norton's support site wasn't much use, why don't you send them an email?
It sounds like it has only installed for one user rather than under "All Users" or for each user (if that isn't stating the obvious!).
Installing again under the other users might help but I wouldn't do that without confirmation from Norton or someone more knowledgable than me about this.