With cicadas emerging, big box stores are overflowing with insecticides promising to kill periodical cicadas. This may be true. If you take a particular insecticide off the shelf and pour it on a cicada it will kill it. But these products will not ‘control’ cicadas. There are millions upon billions of them. There is no such thing as an insecticide that only kills cicadas. They also kill butterflies, bees, and other non-target organisms. It is important that homeowners consider the risks of these insecticides (some) compared to the benefit (none). Cicadas do not last long and pose no risk to people. Insecticides do.
The other problem with trying to manage cicadas with insecticides is that they are generally ineffective. Especially products available to homeowners provide so little benefit that the monetary cost and risk is just not worth it. If you managed to spray a whole tree with Orthene or Sevin for instance cicadas would likely colonize it again within hours or days.
Cicadas cause damage to trees when they lay eggs in twigs. They use a knife-like ovipositor (egg inserter) to insert eggs into thin twigs. This causes slits in the branch that could be 6 inches long or more. This long scar reduces plant aesthetic value, but also weakens branches. Scarred branches usually break and fall to the ground or break and remain hanging in the tree but turn brown.
Trees that are very small or that you just planted this year are at risk if they get many cicada oviposition scars. Cicadas prefer skinny branches (< 0.5 inch) so if your tree trunk is this skinny it could get damaged and this could kill your tree. Other trees will shed a few twigs and go on about their lives. You can protect trees with mesh netting to prevent cicadas from damaging them.