DE is not a poison but rather fossilized algae. Basically its a super fine rock. It passes right through the chicken (or us) but for an insect, it gets in between their body segments and joints and scratches up their waxy coat, causing them to dehydrate to death. The death is physical so you don't see it work right away, but it does work as long as it's dry.
Like any fine dust, you don't want to breath too much of it but once it's down, it's fine.