Conductors on the Stony Point service are required because the present stock CANNOT be worked as driver-only. There is also no agreement to work Sprinters as driver-only (on any service) and therefore conductors will continue to be carried.
The service is a part of the suburban network contracted to Connex, even though it is operated by a VLP train and staff. The latter fact is because Connex does not have any diesel stock of their own; if they did then it would be in use there.
The conductor's duties are to ensure safe operation of the train behind the driver, to release and close the doors (which are now electrically locked and no longer just hand-worked), to view tickets and assist with validation, plus provide assistance in purchasing tickets on board.
The messages on the two-way to the driver can vary from the official "8xxx station work completed" through "Stony Point train right away" and on occasions just "Good to go XXXXX" where XXXXX is the driver's name. You would likely hear similar on any other VLP service where two-way radio comms are used.
The conductor on the Stony Point train does not give the driver the OK to close the doors at present but from next Sunday they may be doing so. Door release / close on the MTH cars is only under the control of the conductor although passengers are still required to slide the doors open once released in exactly the same way as on most suburban electric stock.