The son of the founder of Trader Vic's actually said that they are not the founders of the idea of putting a cocktail umbrella in drinks. I read an article about this in a local magazine once. Someone actually called them up and asked about it. Although they adopted the idea from another restaurant, they also acknowledged that the idea was a Chinese American invention and already existed in Chinese restaurants.
There actually isn't any concrete proof that cocktail umbrellas have anything to do with Polynesian culture. And everything that is said about the parasols serving various purposes are just rumors. The cocktail umbrella was thought of only for the purpose of decoration and nothing else. And they actually have nothing to do with tropical beaches, although that's what most people think of when they get a cocktail with a decorative umbrella.