I think the issue here is something called Dispatch Order. Power plants, in general, are dispatched according to economics, specifically marginal cost. Nuclear has an enormous proportion of fixed costs, and are hardly ever ramped down. Coal is the next-cheapest fuel, while natural gas is the most expensive conventional fuel.
In California, where the OP lives, some utilities own shares of out-of-state coal plants (including LADWP), but the predominant fuel at the margin is gas. Within gas plants, they are dispatched by least-cost, measured mainly by their Heat Rate (Btu's per Megawatt-hour). Less fuel burned means fewer emissions. Since California is a summer-day peaking region, the cleanest gas plants run day/night, while the dirtiest are only called on for summer/daytime use. There are numerous other constraints, many noted in earlier posts, such as ramp-rates (how fast a plant can get to full power) and low-output efficiency, but in general, in California, the cleaner plants run at night, so charging off-peak will minimize emissions to charge your car (or run your dishwasher, etc.).
