Played with the settings and everything, but nothing changed: the little throbber circle spins for a bit then stops with no changes to the page in front of me (and no new tabs open either). At first my download manager was intercepting the links first, so I specifically removed PDF from the list of file types it intercepts... that worked, it started ignoring PDF links, and I thought "now the new PDF extension will work" but nope, nothing.
Uninstalled, and installed Google Docs Viewer. This works great, works the way I wanted PDF Download to work. Only one caveat, and it's for Firefox users: in its settings, "open in new tab" doesn't work, it always opens in the same tab. This may be because Firefox allows you to open any link in a new tab by clicking the middle mouse button (or wheel) instead of the left button, and this may be overriding the Reader's setting. So for Firefox users, if you want the PDF to open in a new tab, just click the link with the middle mouse button as usual. Displays great though.