For example, if I buy a base that generates GenMat for the monsters advisor, and I think "it'll be cool to make something monster themed", will other players raiding my all-monsters base get the GenMat for the advisor who does monsters?
I believe so yes. If you notice when you raid there is a certain advisor that gets progressed. Quiet sure it’s the genmat they builder is getting
The genmat of your base determines all genmat related exchanges unless your outpost becomes legendary or whatever the term for those white arrow bases is. In which case the raider gets all 5 types of genmat.