I can't tell you the exact insecticide that your neighbor is having used for their trees, but I can tell you that the products labeled for home landscape use for the Bronze Birch borer are acephate, clothianidin, imidacloprid, pyrethroids, and chlorpyrifos (which is a restricted-use product). 

Birch flowers flowers may be visited by pollinators as an additional food source, therefore externally sprayed or systemic pesticides may present negative, non-target impacts. Impacts are minimized when insecticides are used after the trees are done blooming.