If the arrest was recent
Start with the county jail
This is the key point in California: someone just arrested is in a COUNTY JAIL run by that county's sheriff, NOT in CDCR state prison, so CIRIS will not show them.
California has 58 counties, each running its own jail system; many large sheriffs publish an online 'Who's In Custody' / inmate lookup (for example Los Angeles and San Diego county sheriffs), but there is no single statewide county-jail search.
For a recent arrest, use the arresting county sheriff's inmate lookup or VINE.
California's statewide VINE service (approaching full county coverage, provided by county offices and CDCR) gives near-real-time county-jail and prison custody status.
Most large California county sheriffs (e.g., Los Angeles, San Diego, Orange, Sacramento) offer an online 'Who's In Custody' jail lookup; statewide VINE fills county gaps, but for a few small jails a phone call to booking is the reliable path.