SCT Controller reported Aircraft X failed to follow ODP resulting in an MVA violation and an airborne conflict.

Narrative

Aircraft X was departing SDM on the SDM Runway 8 ODP. This departure is an immediate left turn to the west with a climb to 4000 [ft]. Aircraft X departed and continued eastbound into a 5000 [ft.] MVA. The aircraft checked on with me. I issued a low altitude alert. I was attempting to evaluate the situation with arrivals to SAN for a turn and/or climb to the west away from terrain. I issued a turn to heading 280 and later a climb to 5000 [ft]. I was concerned about 5000 [ft.] due to Aircraft Y inbound to SAN at 5000 [ft.]; but I decided it was better to climb out of 4000 [ft.] for MVA. I issued another heading for the aircraft to fly upon reaching 5000 [ft]. I continued the climb to 15000 [ft.] once I had evaluated the situation more and was recovering. I handed the Aircraft off to TIJ Approach. SDM Tower indicated later that they had issued the ODP and had asked the pilot(s) if they understood it. The aircrew indicated they understood the procedure. Separation may have been lost with the Aircraft Y on SAN arrival due to slow rate of turn of Aircraft X. Recommendation [is to] evaluate the possibility of issuing 5000 [ft.] to SDM Runway 8 departures. The ODP does turn them into lower terrain to the west; but I have seen this departure go bad on several occasions and it might be safer if the aircraft were initially climbing to the MVA that is directly in front of them as they depart. It would still be a MVA violation; just a 'safer' MVA violation.