Legal Question in Criminal Law in California

The court will not notify them. They might subscribe to a "background check" service that would tell them. My best guess, not knowing where you work, is that like most employers they only run "background checks" before they hire you. Consult a lawyer about not getting convicted.

It depends on who your employer is.

Nobody 'notifies' anyone of your conviction except to enter it into the computer data base[s] and court records, but any employer, or insurer, can check the records to find it.