How does a switching power supply reduce its power output?
The power supply's job is to maintain a constant voltage. When the CPU "switches off logic", less current is required from the power supply to maintain that voltage. The current demand from the CPU is constantly changing under normal operation, so switching power supplies have feedback mechanisms to adjust the current they produce such that they maintain the correct output voltage. Thus, if the CPU enters a special low power mode, the power supply need not do anything extraordinary. It just does what it always does: maintains the output voltage.