Hello Anne, the recommended (by me) method is to scrape every tile clean from the top down and finally the gutter/downpipes etc. Not the most favourable job in the roofing world but needs to be done sometimes. Treat with an anti fungal solution which deters any future growth, unfortunately the rate of growth depends on where you live!
I would never pressure wash tiles as depending on the make they can be extremely brittle, usually the older the weaker.
McLean roofing and building ltd