Question about inbox Notifications. Here is what I currently see in my Inbox on 7/30/19
If the task is assigned to you, then the auto-promotion feature kicks in: if you push the task to Later in My Tasks, it will automatically come back to Upcoming 7 days before the due date, and then in Today on the due date 
See task auto-promotion section on How to Get Started With Asana My Tasks | Product Guide • Asana Product Guide
1 Like
Hi @Sherpa5 and welcome to the Forum!
As @Bastien_Siebman explained, Tasks with due dates that have been marked as Upcoming or Later will automatically promote through as they approach their due date.
Regarding the Inbox Notification, when a task assigned to you is approaching its due date you will again receive an Inbox Notification.
I hope this helps! Have a great day! 