That’s odd because I do have settings being saved to ~/Library/Sprinklers/LocalStorage. Does this folder exist on the system with the app installed?
Also, which version of OS X are you using? By the way, Apple is terribly slow at updating the OS X app. They emailed me yesterday letting me know it will be a while before they review 1.1.8 (latest on store is 1.1.6).
Just for the sake of debug, I created that folder structure manually (i.e. added Sprinklers/LocalStorage to my ~/Library), but I still get the same result, and those new folders stay empty.