Summer cuttings are best taken in July and August.

Usual method with this shrub (photinia Red Robin) is ripewood cuttings in autumn.

Here in Scotland I have had success with heel cuttings in a pot at the end of July and covered with a plastic bag, then placed in the cold frame. They were ready to pot on in the spring when they had developed roots. Sorry I do not know how you would do cuttings in the autumn, but maybe you should try both as that gives you a better chance of success. New Photinia Red Robins are quite expensive.