Auto-promotion only works on due dates (not start dates) I believe. (See Start Date Tasks in Today’s My Tasks - Product Feedback )
I, too, struggle with an optimum way to use due dates vs follow-up dates. Asana doesn’t seem to have a convenient, friction-free way to get this level of granularity, so I end up with tasks where the “due” date is really just a “follow-up” date, and after follow-up, I change the due date back again. It works, but I feel this is an area where Asana could be smarter to help my flow.
To be clear, the problem (truly, it’s a minor problem) is that my Upcoming list is a mix of tasks that could be worked on now and tasks that need a follow-up on a specific day in the future.
Hopefully that makes sense…