An inbound Air Carrier and a VFR helicopter had a conflict during the use of visual separation between the two aircraft.

Narrative

Aircraft X; a CRJ; was inbound from the south to land. He was descending to 40 for traffic. The traffic was a helicopter; Aircraft Y; who departed the airport and was eight miles South; VFR southbound. He was level at 3500. Traffic call was issued to Aircraft Y several times without a response with ten miles separation. At six miles separation the helicopter checked in with another radio. I asked if he got the traffic call of the CRJ at 40. Aircraft Y said he had him in sight. Aircraft Y was told to maintain at or below 3500 for the traffic at 4000. Aircraft X (@4000) was given the traffic at 12 O'clock and four miles at 3500 southbound. He called the traffic in sight. I gave him instruction to maintain visual separation from the helicopter and descend and maintain 20; report the airport in sight. He read back that he would. Aircraft X descended through altitude of helicopter; in a way that made the helicopter question the CRJ's altitude. He sounded a bit surprised at the regional jet's action. On the ground; the pilot of the CRJ called and was concerned that he had broken some kind of separation. He also seemed excited and a bit shaken. He seemed to be unsure of what he had done to make this situation happen but he knew that he got close to the helicopter. I advised him he could have waited a bit before descending or a slight turn to assure he complied with his instruction to maintain visual separation. He said he knew that but it seemed like an optical illusion and that the helicopter was just hovering; and that the traffic ended up being closer that it appeared; possibly from lights from the ground or airport lighting. At some point he received a RA and followed that which must have put him in a dive to avoid the helicopter. As a controller; be aware of lighting situations on the ground during evening hours. The pilot had a very thick accent and maybe the instruction should have been delayed until the traffic was no factor.