They are, yes.
Parks run a number of journeys on behalf of Scottish Citylink, similar to other contractors, but do actually run co-ordinated journeys as part of their City2City network on their own back. There are different fares from their Citylink operated journeys and such like. This is a hangover from the Joint Venture competition investigation following the agreement between Stagecoach and ComfortDelgro after the bloody competition following the launch of Megabus. So as such, Parks journeys (marked as operated on the Citylink timetables) are independent of the other journeys.