Hi there. Today I created a project and assigned it to an employee with a due date. I also assigned to myself as another project user. This task is showing under my project, but not the assignee. I have done this with numerous other tasks but know this is happening.
Welcome 
What does that mean? Did you assign to yourself or to a second account of yours?
Hi @Michelle_Hurlbert and welcome to the Forum! 
Sounds like you might have added a due date to your project but not to the [tasks](: How to Complete Task Fields in Asana | Product Guide • Asana Product Guide) itself?
Can you share an example of one of these tasks assigned to you?
Looking forward to your reply!