Blizzard has released a couple of updates about the new downloader tool and how it's currently operating. First, this note about where the downloader is currently storing files:

We are aware that the background downloader is currently delivering data to the desktop of some players. Early next week we will deploy a tools patch which will move any data delivered to the desktop to the proper location.

We recommend that you do not move the data yourself, but allow us to move it for you during our next tools patch. Otherwise, the background downloader will fail to find the data, and begin background downloading the data again.

If, for whatever reason, you must move the data, please contact our technical support team first. There are a number of steps that you will need to take in order to successfully move the data and prevent future problems.

As before, Macintosh players who wish to background download will need to run the background downloader manually. Information on doing so can be found here:

Secondly, this note about which download stages this problem is currently affecting:

It can occur with both data portions until we release a new background downloader update to correct the issue. We're currently working on the update to fix the problem, but we have no estimate as to when it will be released.

Thanks to Blizzard for this info about the new downloader, and hopefully we'll see a fix soon!