photinia belong to the rosaceae family, that of the roses.
similarly to your roses they do not like excessive water around the roots and such stresses can cause fungal infections -hence your black spots similar to those seen on rose leaves.
the difference being that photinia is evergreen, so infected leaves are not shed in autumn. but you will find an infected shrub will shed the majority of infected leaves in spring, which should be collected up and burnt.
you can use a spray fungicide such as multi rose which will begin to control and alleviate the issue.
if choosing new photinias to plant pay close attention to the species you are buying.
photinia serrulata is highly prone to black spot, where as photinia x fraseri shows far more tolerance to black spot.