Here is a closer pic.

This is exactly the reason I always suggest people take pictures on a cloudy day. I presume this is a St Augustine lawn, but I can't really be sure.

20 minutes per day is exactly the wrong way to water. The watering mantra is deep and infrequent. Deep means 1 inch of water all at once. You can measure 1 inch using a cat food or tuna can. Place several around the yard and turn on the sprinklers. When the last can is full, that's how long you need to water. Infrequently means not every day. When the temps are in the 70s, infrequent means once every 3-4 weeks. In the 80s, water every other week. In the 90s water once per week. Above 100 you might need to go to watering once every 5 days, but NEVER water more frequently than that. Special exemptions are granted if you live between Banning, CA and Junction, TX south of Green River, UT. That area has a combination of soil, sun, and lack of shade issues which may allow watering every other day; however, I know people in Phoenix who water once a week and they do just fine.

Take a picture of the grass with the camera about 3 inches away from the blades. If you have some yellowing or poor looking blades, get a pic of those. The pictures you posted look weird because I don't see any dead grass between the living grass.

Also if looks like you are mowing on the mower's lowest setting instead of the mower's highest setting. Change that right away. St Augustine does much better when it is taller. I have an experiment going on with unmowed St Augustine. After nearly 2 years without mowing, some of it is 32 inches high. Much is still down around 9 inches. Most is in between. All of it is healthy looking without any fertilizer and very little watering since Oct 2011. I've not watered for 3 weeks and just left town for a week. Temps are near 100 every day in that area, and I'm not worried. But I'm not suggesting you go to that extreme. I'm trying to prove that taller St Aug is healthier and needs much less water.