It is common for us (so far) to assign multiple people to a single task. When the task is assigned, it shows up in the task list for each user. When one user is done, they mark the task as, “Done with my part.” This removes the task from their “To-do” list, but it does not show up in their completed list. I have tested this, and it appears the reason is because the overall “Task Status” has to be set to “Complete” before it will appear in the users completed task list.
So, tasks will only show up in the completed items area when all users are done with the task, and not when only a single user is done with their part.
This creates an inconsistent user experience.
Also, if the user needs to revisit the task later (they are not actually done yet), they have to navigate to the project and locate their task.