The way I learned this was "in legal, out legal," meaning that you are not allowed to be driving in the intersection while the light is red (aka you have to be finished transiting by the time the light changes).
Is this not the law in California?
In my state you are allowed to exit the intersection while the light is red but may only enter while it's green or yellow. In driver's ed they taught us to enter the intersection while waiting to make a left turn so that we could complete the turn after the light turned yellow/red and opposing traffic stopped.
My understanding is that California has two relevant laws for this discussion:
21453 (a) which prohibits crossing the stop line when the light is red [1]. And 22526 (a) which prohibits entering an intersection when the exit isn't clear. [2]
You have to be able to clear the intersection if you enter it, and you have to enter it on green or yellow (except for turn on red after a stop), but you don't have to clear the intersection before it goes red.
Common practice (which might not be 100% legal) for unprotected lefts on green (where space permits) is for the first car to fully enter the intersection and the second car to roll over the line a bit, then for both vehicles to clear the intersection when opposing traffic stops which may be in yellow or red. The driver that's only a bit in the intersection can make a judgement call and stay slightly encroaching rather than clear the intersection if clearing seems inadvisable because opposing traffic was slow to stop.
[1] https://leginfo.legislature.ca.gov/faces/codes_displaySectio....
[2] https://leginfo.legislature.ca.gov/faces/codes_displaySectio....