The new button should be placed in the column container under the tasks/cards and it should add a new task.
This feature is the same as the "Add a card" button in RadTaskBoard for WinForms.
Currently, the card model is added to a group when initially added to the ItemsSource of RadTaskBoard. Also, it can be moved to another group by drag/dropping on it. However, if you update the card model property that is assigned to the GroupMemberPath of RadTaskBoard, then the card is not moved to the corresponding group in the UI.
To work this around, remove the card object from the ItemsSource, update the group property and then add the card object back in the ItemsSource.