Hi mtrosper,
Did the supervisor connect all users’ task lists into his/her Outlook?
Please ask the supervisor to check whether he/she input the right person when he/her create tasks for them.
Based on my test, when I connect all users’ task lists into one Outlook account, then I create tasks in these task lists and assign them to different users.
When SharePoint sync them back, these tasks are assigned to the right people.
You can try to use a SharePoint site instead of mysite, then create a task list, check the effect.
For more information about create tasks on a SharePoint site by using Outlook, please refer to the following article:
View and create tasks on a SharePoint site by using Outlook
http://office.microsoft.com/en-us/outlook/HA100820301033.aspx
Hope this helps.
Rock Wang
Rock Wang– MSFT