An electronic device with a touch-sensitive surface displays a user interface of a first software application that is updated at a first display rate. While displaying a first frame of the user interface in accordance with the first display rate, the device detects respective movement of a touch input across the touch-sensitive surface. An application-independent touch processing module of the device selects a respective touch location of the touch input that was detected during the respective movement to identify as a representative touch location for the respective movement based on touch-processing criteria for the first software application, and sends to an application-specific portion of the first software application touch location information for the touch input that identifies the respective touch location as the representative touch location for the respective movement. The first software application updates the user interface in accordance with the touch location information.