The settings are for each individual student in the course. When an individual completes the activity, then they can go on. (Feb 11 question).
Make sure that the student has actually fulfilled the activity. They might need to finish the post and then return to the course page, not by backing up in the browser but through the links at the top of the page. Also have them refresh their page. Sometimes a browser will save the old view of a page and with a refresh they will see the next section. (Feb 18 question).