https://www.imore.com/how-set-and-use-emergency-sos-your-iphone-ios-11
According to this iMore article by default the iPhone 8, 8+ and X require the sleep/wake button AND one volume button pressed to active. So that is two simultaneous button presses. The 7 and older iPhones just require the 5 sleep/wake button presses.
In all cases the auto-call setting must be set to ON or a screen slider is required to place the emergency call. Apple has provided the tools to prevent most accidental emergency calling but getting users to use those tools is another problem.
Of course the park could help by fixing/replacing excessively rough coasters.