According to TfL's response, once pressed, emergency buttons on Passenger Help Points (PHP) ring through to the station operations room. If not answered after a certain time the call will be routed through to the London Underground Control Centre. TfL is currently making improvements to the emergency service to ensure that all emergency buttons are routed through to the control centre when pressed so that the caller can receive immediate help.
Turbulence can appear suddenly and isn't always detected by onboard radar systems, so there may not be time for the pilots to put on the seatbelt sign.