Do you mean Photinia ?

I wonder if you mean that too..sometimes it is known as 'Red Robin' here as well,being the variety of Photinia..

If that is the plant you mean then I think the recommended time is after the red tips have turned green in early summer but I give my Photinia Red Robin hedge very light trims to keep it in shape virtually throughout the year and this seems to stimulate attractive new red growth month after month.

In colder climates, they can be trimmed several times in the summer to keep the red tips coming. In mild winter climates, like mine, we trim in early fall, to get red tips for the fall and early winter, and again in early spring for a spring show. Pruning can be done in summer for size control, but usually doesn't result in much red, because the nights are warmer. In fact, it is so hot here in summer, that we only prune cautiously, because the bare branches tend to burn.