You don't get any tasks populated in the My Tasks Web part on your My Sites.
You have everything configured properly as far as permissions. You see this in the event logs:
Event ID 8077
"There are no instances of the Work Management Service started on any server in this farm. Ensure that at least one instance is started on an application server in the farm using the Services on Server page in Central Administration."
The service not started.
Start the service: Central Administration -> System Settings -> Manage Services on Server
Choose the server where you configured the Work Management Service to run when you installed it and Start it by clicking on the start button.
Run a crawl.