The shared mode is recommended for teams which use a single Board to plan work.
When the option 'Shared mode' is selected in the Scope synchronization view, moving cards between different timeboxes will update the fields of the selected box.
When you switch to the 'No synchronization' from a different mode, your tasks will remain in the last place on the Board.
The default values of new and existing boxes result from the configuration templates and can be changed at any time - Program configuration - Board - Synchronization.
To learn more about the Board go to the Working with the Board page.