As I understand it, ET is trying to quantify how much water (inches or mm) will be lost from the soil (evaporation) and plants (transpiration). So conversely ET tells you how much irrigation water will need to be applied to replace that lost water. Since Hargreaves-Samani does not take precipitation into account, my assumption is that you simply subtract precipitation from ET to get how much irrigation water is needed.
For altering watering, IMO the best way is to measure water output per zone (inches or mm / minute) and then use ET (minus precipitation) to determine how many minutes to run. Measuring water applied to each zone can be done with cans placed on the lawn. A simpler alternative is to figure an average water output for all zones and then adjust them all up/down by some ratio (percent) as ET is higher or lower than this average. Another method is to look at historical ET data and figure an average (for the whole summer or maybe just July) and then use that as a baseline to compute if watering should be increased or decreased.