Hi TeacherHaley,

I might be able to help. What type of grass do you have? Warm season(Bermuda) or cool season grass(fescue, rye). I assume in AZ you have a warm season grass like Bermuda. If this is so, Bermuda goes dormant in the cold months and doesn't take up water. It also becomes brown. It is not dead, but will green up when the weather gets warm again and then it will again need water. I am sure you could almost turn off your water off and it would not mind. The browner the less water. Shrubs are different keep watering them. Is you shrub watering separate from your lawn watering. It should be. Your shrubs take less water than your lawn when it is growing. A rule of thumb is in the peak of the warm/hot season you would water the equivalent of one inch of water on your lawn each week. Maybe more in AZ, but in winter one inch of water maybe in two months. You will learn what is best for your area so keep paying attention until you feel comfortable that nothing is stressing. Cool season grasses are something else entirely especially in your area. Hope this helps. GL. Aloha

teacherhaley, cooler temperature alone cannot account for the described wet condition after an irrigation. If nothing was changed, then the water sprinkled on would move downward and outward in the soil exactly as it did before.
I suggest that you operate the system manually, as needed. You can determine this by probing the soil and observing the grass blades. When you do decide to irrigate, turn on the sprinkler manually and note the time. Shut down the system as soon as water starts to pond on the surface or runs off the lawn. The time this takes to occur is the run time of your irrigation system. The interval between irrigation events is determined by the external conditions of temperature, transpiration by the grass and evaporation from the ground surface. You can determine the interval between rrigations by probing the ground and examining the grass.
The issue has been addressed by McCarthy, Cisar and Dudeck in a paper "Irrigation Management Practices for Florida Golf Courses". As I recall, they made recommendations for different areas of Florida for each of the 12 months in the year. Their recommendations are a good place to start firming up your own irrigation schedule.

teacherhaley, I meant to add that you might be able to find similar information relevant to your area from your County Extension Service.
The omission is regretted.