Does a negative feedback mechanism result in reduction or increase of the initial stimulus?

Negative feedback mechanisms will reduce the deviation from the set point, or, to use the terminology from the question, they will result in a reduction of the initial stimulus.  
Look at the example of body temperature, 37 degrees C.  
If our temperature increases by 2 degrees to 39, thermoreceptors detect that change and notify the hypothalamus that our temperature has deviated from homeostasis.  The hypothalamus then promotes actions like sweating and vasodilation of the surface blood vessels to get heat to the skin and remove it via evaporative cooling.  Thermoreceptors detect that our 2-degree deviation has been reduced to a 0-degree deviation (i.e., we are back to normal temperature), and the hypothalamus puts the body back to resting state.
If our temperature decreases by 2 degrees to 35, the hypothalamus promotes shivering and vasoconstriction.  This warms the body and keeps heat near the vital organs.  Again, once the 2 degrees has been reduced to 0 degrees, the body goes back to resting state.
Opposite directions of temperature change, but the initial stimulus was still the same amount: 2 degrees.  Since the stimulus needed to be brought back to 0, both of these mechanisms are negative feedback.  They both reduced the deviation from normal body temperature.