I don't have the California Vehicle Code in front of me, but I'm pretty sure about this because the situation arose during my road test to get my first license (yes, I still remember this, even though it was almost 40 years ago!). I had entered the intersection to turn left, and when the light turned yellow, the tester lady said "clear the intersection" or words to that effect. (I passed.)
Anyway it has to be that way -- you can't have cars stuck in the middle of the intersection while cross traffic tries to go around them!