As far as I'm aware, the only time an ATCO is responsible for terrain separation is under Radar Control. Under any other type of service, it is ultimately the pilot's responsibility.
ATSUs will set a level or levels below which RAS will be terminated or not offered.
Under RIS, radar vectors will not be supplied below the ASA/MSFL except under strict conditions such as, actual emergencies, short pattern circuits or radar to visual approaches inside 10nms from the airfield. Although these are military guidelines, I would imagine the civil ones are much the same??? Anyone else able to shed any light?