That quest does not add sockets to the item. What it does is allow you to exceed the visible slot limit, to attach a total of 5 materia. If the item in question has 2 slots, then without having done that quest you can only attach 2 materia to it. After having done that quest, you can add 3 more - though forcing extra materia on has a chance to fail.

Of course, if you have forced more materia onto the item, those materia have to be displayed, so it appears as though it had slots added.