When you set a "Due date" for an action it is still a next action, so it's normal that it's shown in the Do section. The due date is meant to be a deadline, but it doesn't mean you can start working on it before the deadline (you can start on it asap, as with any other next action). If you want to set a date and only see that action in the due on the date set, then use a "Calendar" date. You can also use an "Start date" (deferred), and the action will be hidden until the date arrives, when it will start be considering "next" (and will show up in the Do).
We are working on the docs for 2.0 but you can check this post about the different kind of dates Zendone manages.