This issue and the one mentioned in topic Improvments for the “Today actions” list by Olega007 make the Today feature hard to use in my experience. I think it would be best if this section was just an overview of actions / projects of 3 different types:
-actions / projects that were dragged manually to this list in the 'Today' overview;
-actions / projects with due dates today under the 'Today' overview;
-actions / projects with due dates in the past under the 'Past Day's Actions' overview.
If the system would automatically update the lists based on any changes to these parameters that would make it most useful in my view.