Look for young crawlers on the undersides of magnolia leaves starting in August when eggs are laid. At 1/25 of an inch, the nymphs are very hard to see without a magnifying lens. Sometimes you can find an infestation by tapping a leaf or twig over a sheet of white paper.
Use a sprayer to hose down crawlers on trees on which you found infestations. Use an insecticidal soap or horticultural oil, or both. Make coverage very thorough, because crawlers can hide under dead adults' exoskeletons and inside bark crevices.
Repeat the application several times during September and October, due to the protracted period of crawler emergence.
Target dormant scale surviving through the winter by spraying the tree with horticultural oil in late winter. The lack of leaves helps you to be thorough in your coverage. Make sure the temperature is above freezing for the oil to be effective.
Drench the soil at the start of May with an imidacloprid-based insecticide, such as Merit 75 WP or Bayer Advanced Tree and Shrub Insect Control. Pour the insecticide into the soil within a foot of visible roots or the trunk.
Soak a toothbrush in a mild detergent solution and scrub the waxy shells of the adults off the branches. The detergent should make them slippery and fall off. If you want to be environment-friendly, use a 30-to-1 dilution of Simple Green nontoxic all-purpose cleaner. The shells will start appearing in late spring or summer and become quite large, easy targets.