This is a great question, with so much information on the internet you can sometimes come away from researching thinking I still don't know the answer.
My answer is based on many years of experience and knowledge in the stone restoration industry cleaning many 1000s of paving in the domestic, commercial and industrial sectors.
Any chemical not only patio cleaner can be harmful to plants if not used properly. When using patio cleaners prevention is better than cure, first of all if the patio run off is going into a flower bed simply give the flower bed soil a good soaking before hand. If the patio meets the lawn give that a good soaking that way your grass will be fine. If applying next to your prize plant you could give that a good watering and cover with a plastic sheet to protect from overspray. If spraying patio cleaner onto paving don't do it on a windy day as the wind will carry overspray. If for whatever reason you do get some on your grass or plant just give them a quick rinse down and they will suffer very little damage.
Our patio black spot remover Instant Clean is biodegradable, child and pet safe once dry.
Our other patio cleaner Stay Clean is a Wet and Forget type product, simply spray on and leave, no scrubbing or rinsing required. Reapply once a year, it kills moss, algae, mould and mildew. Use the same precautions ie; Wet flower beds, if patio meets grass simply give the grass edge a soaking with water. If applying via a garden pump up sprayer do it when its not too windy to prevent the overspray travelling to places you don't want it. If your worried about your flowers or plants give them a good watering before, you could even use a plastic sheet to cover.
Stay Clean is biodegradable, child and pet friendly once dry. Here is a great guide to help you decide the best method for you: How to clean your patio