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No, I think you're using it correctly. That feature was added to the iPhone app later (in v1.5.2 according to the release notes) -- it initially worked like the desktop app. Maybe that behavior will appear in the desktop app if enough people send in feedback requesting it, or the developers think it is a good idea on their own.

In my own usage on the desktop, I find the due soon styling to be sufficient, especially in conjunction with a context mode perspective for showing stuff that is due in the near future. (Group by due, sort by due, due soon, any flag, any duration) Because I can't do that on the iPhone, having the due dates shown next to each action is more essential there.