I believe you should use WebSocket to automatically refresh the user's screen.
You can use this marketplace module supported by Mendix:
And if you don't want your application to communicate with another service, you may want to go with this one:
I can think of three options:
1. Microflowtimer (see market) which should refresh an object of your taskinbox
2. WebSocket as Slavko mentioned
3. Add a refresh on your datagrid2 object such as:
But which solution should you pick? The option of the datagrid2 can be done within seconds and requires no additional modules or widgets. It is however more data intensive, since no matter what you will always refresh the grid. The option with the websocket (Pusher) however can be configured on such matter that refresh only will happen when there is new data (tasks) to be shown.