Private URL not generated correctly when sitewide download method is set to Public

I may well be doing something wrong, but this module isn't working quite as I expected it to. Basically, when I view the results of a submitted webform with a file, the URL to the file (sites/default/files/private/something.txt) is not being overridden by a private version (system/files/private/something.txt) when the sitewide download method is set to Public.

Steps to reproduce:

1. Make sure that the sitewide download method is set to Public.
2. Install webform and webform_private_upload.
3. Visit the WPU configuration page so that the private directory is created.
4. Create a new webform including a file field whose target directory is inside the private directory.
5. Submit the webform once, uploading a file.
6. Check the results. If you look at the href attribute of the download link at this point, you'll see that it's not the correct private URL. If you click the link, it won't download (b/c the .htaccess prevents it).

As I said, it's quite possible I'm doing something wrong …but as far as I can tell my configuration is pretty standard. Is anybody else experiencing this issue?

Thanks!
Adam