If that is unchecked, the assignment is set to the right group, and students are in groups, I am unsure why it is showing individual names. On my end, the only time I have seen that is for students who have not joined a group or that checkbox is unchecked. At this point, I might suggest that the teacher submit a help ticket. I would highly advise that they include a screenshot similar to the one I shared to show the Group settings for the assignment. This way, if there is a glitch, they can try to look at the course and assignment.
I have noticed that I tend to have more issues when students self sign up rather than be assigned (some of the issues caused by students). Self Sign Up is definitely easier on us, but an alternative is to do the sign-up off of Canvas, then the teacher makes the groups. One way to make this easier...CSV importing. If you go to the People page, then create a group set (but not groups), there is an Import option in the upper right. This will pop up a menu to import a file. Near the bottom is a template file that can be downloaded. This template is course specific and will include a list of all students (and multiple columns of pre-set data) currently enrolled in that course. You may need to expand the column widths, but the final column is "group_name". The teacher just needs to put group names into that column before importing that file (do not change any of the information in the other columns). It will create groups based on the names and assign all students with the same group name into that group. This at least eliminates the tedious task of manually putting students into groups on the group page.
More info here including the steps for best practice: https://community.canvaslms.com/t5/Instructor-Guide/How-do-I-import-groups-in-a-group-set/ta-p/41779...