ZLA Controller reported SCT failed to follow letter of agreement resulted in aircraft being in a higher MVA and a CFTT event.

Narrative

At the time of the incident; I was combined with one high sector and two low sectors. Due to staffing issues at SCT several abnormal operations were happening with all LAX arrivals on one flow rather than the normal two; and several reroutes were being issued to aircraft landing SNA/LGB flying abnormal routes.The aircraft departed from PSP and appeared to be vectored by SCT as they do for their own traffic prior to clearing the A/C (Aircraft) direct to YUCCA per our LOA (Letter of Agreement). These A/C are supposed to receive preferred routing via the YUCCA SID which puts them on routing similar to V386 to PMD. When checking in I noticed this aircraft appeared to pass YUCCA but did not continue onto the SID appropriately towards SOGGI as they should; instead the aircraft continued westbound towards an area of high terrain in the sector. I turned the aircraft to a 345 heading to start them north as I knew they were close to high MIAs they were below while pulling up the MIA map. Once I pulled up the MIA map I noted that they were at 11;500 with the MIA area they were in being 12;000. I issued the low altitude alert phraseology; along with reissuing the 345 heading towards areas of lower terrain and advising the pilot to expedite their climb. The A/C was observed going through 12;000 via Mode C and exited 12;000 MIA block laterally as well. I asked A/C what their next point of navigation was and they said they were direct TILTS which is the arrival routing for their destination rather than the appropriate routing via the YUCCA1 SID.The MSAW alert never activated during the event.I issued appropriate routing and further climb to the aircraft once they were clear of traffic conflicts.Ensure tower is issuing appropriate SID to aircraft; which separates them from appropriate terrain.