So, this is an interesting question, because technically Chubby Buttons does not specifically communicate with any headphones, but it works seamlessly with all of them! How is that possible?
Here's a short video that breaks it down:
In essence, your Chubby Buttons is seen as a bluetooth keyboard by your smartphone, and your phone can have up to 8 bluetooth inputs. Since your smartphone sees Chubby Buttons simply as a keyboard, it really has no affect whatsoever as to how you choose to listen to your music. You can have wired headphones, wireless headphones, or a big bluetooth speaker. Ultimately, the best answer is that your Chubby Buttons has no affect on the bluetooth audio output, so de facto -- it "works" with all headphones :)