1. A computer program product for controlling interrupt processing in a computing environment, the computer program product comprising: a computer readable storage medium readable by a processing circuit and storing instructions for execution by the processing circuit for performing a method comprising: determining that a CPU-facing pending indicator has been set indicating an interrupt request by an adapter of the computing environment; presenting the interrupt request to an operating system, the operating system to process one or more set event indicators corresponding to the interrupt request and one or more other set event indicators corresponding to one or more other interrupt requests; resetting, in response to the presenting, the CPU-facing pending indicator indicating to one or more processors that an interrupt request is not pending, wherein a hub-facing pending indicator remains set to indicate to a hub an interrupt is already presented and to suppress other interrupt requests from being made pending; resetting the hub-facing pending indicator, responsive to a change in a control mode to allow another interrupt request to be made pending, the change in control mode responsive to a determination that event notifications are arriving at a rate faster than can be currently handled and that another interrupt request is to be presented allowing at least one other processor to process set event indicators; determining that the CPU-facing pending indicator has been set indicating another interrupt request has been made pending; and presenting the another interrupt request to one operating system of one or more operating systems.