Hi Laura,
I re-tested it today and found a difference depending on how I did it.
Scenario 1: If I login as another user, then assign a task to myself, then set it to In Progress status, it all works correctly and moves to my Working On tab.
Scenario 2: If I assign a task to another user, then login as them, then set it to In Progress status, the issue occurs and the the assignment status goes to Done (and the task is not visible on either tab.
I will update my Support ticket and see what they think, but it could just be a side-effect of the Login-As feature.
Regards, David