Ponding of water around the sprinklers can be a symptom of clay soil if it's being overloaded, as in too much water is being sprayed out too often for it to dry out. If this has been a constant issue for several months, however, it's more likely a landscaping issue, as others have pointed out, especially if neighbors have the same kind of soil but don't have ponding. Does your washing machine drain into the system? I'm a little fuzzy on the specifics at the moment, but Texas allows for graywater to be discharged directly onto the yard using a flexible hose, unless your particular jurisdiction prohibits that. This would help reduce the amount of water going into the system and should decrease how often the sprinklers go off, especially if you do laundry often.
The rest of my post provides additional information about this particular type of system, mostly in response to Mitchell-DIY-Guy's research into the topic, for anyone that's interested.
In my area of north Texas, aerobic treatment units (ATU) with spray distribution are fairly common because we have a lot of clay soil. Clay does not drain well. You can put lateral lines in clay but you need more line to spread out the effluent over a larger area and the effluent has to be released in doses throughout the day so the soil doesn't get overloaded. At that point it is often cheaper to install an ATU and a couple of sprinkler lines. How much space you have is also a factor, which can explain why some properties with better draining sandy/loamy soil have ATUs because they don't have the room for lateral lines.
The idea of a properly functioning ATU is that it's basically a miniature wastewater treatment plant. It includes sedimentation/anaerobic digestion, aeration/aerobic digestion, clarification, sludge recirculation, and disinfection. The effluent coming out of the sprinklers should be chlorinated. There's much debate about the effectiveness of various chlorinators, and chlorine tabs versus liquid chlorine and how well any of it actually works. Any manufacturer of such products will, of course, tell you their product is superior. Some aerobic system manufacturers even claim (or have claimed in the past) that the effluent out of their system will be so clean you can drink it.
Part of the disinfection process supposedly also can involve UV light from the sun, so water on the ground in the sunlight will be further treated before it infiltrates the soil. Obviously water in the shade or at night won't receive this benefit. One of the advantages of spraying the effluent on the surface when you have clay soil is that some of the water will (should) evapotranspirate before it infiltrates further into the soil, thus reducing the hydraulic load of the clay soil.
