Unless you've already set up alternative HTML template sets, you'll need to overwrite the original files instead of using a subdirectory.
Note that there's a bit more magic to alternative HTML template sets than just making the subdirectory.

The control panel isn't quite smart enough to determine whether or not it's set up right. It just assumes that it is.
Copy the public_common file into the subdirectory. Edit the copy - on line 12, you'll see:
$template_html{"PUBCOMMON"} = "";
Place the directory name between the double quotes there, i.e.
$template_html{"PUBCOMMON"} = "test";
Without this change, the alternative HTML templates won't get loaded properly.