TouchDown stores all contact information in its own internal database that's separate from the internal contacts database that Android uses. You need to open the contacts app in Touchdown > tap menu > tap copy & paste. To make sure Android's contact app stays up to date, you will need to go into Touchdown's advanced settings and enable the update contacts to phone option.
To provide the feature you are asking about, Google would need to work directly with Nitrodesk to ensure the two are always in sync from a compatibility standpoint. Google should not be expected to do this.