Legal Question in Real Estate Law in California

Whenever the lease or rental agreement says it begins.

There are actually two significant dates: (1) the date upon which the old, out-going tenant is no longer obligated to pay, and (2) the date the new tenant's obligation to pay begins. If #1 occurs before #2, the rent is "prorated" three ways" to the outgoing tenant, to the new tenant, and, during the gap, the landlord in effect pays himself. Generally, date #1 is determined by the later of when (a) the tenant actually vacates, often signified by returning the keys to the landlord, or (b) notified the landlord in writing as his move-out date. Date #2 is the date the landlord gives possession to the new tenant, and handing over the keys is symbolic of giving possession.

It begins whenever the parties agree it does. That's what you contract is for.