Seems to be a problem with the workaround.
I create a .c and .h via the templates. The .c shows up in the editor but the .h doesn't. So, from the projects toolbar I right click the folder, add files, select both files and add them. They are both in the project now, but when I open the .h it is set to plain text mode instead of C/C++ mode.
I think the same thing happens if they are added from the project properties menu, which is strange because adding a tree at the start worked as expected. I wonder if the auto-mode detection is broken.