Good news, even with heavy clay soil and automatic sprinklers this can be done.
In order to determine how much water your sprinklers are getting out, you could do a can catch. Place small, shallow empty cans (such as tuna) around your area to be tested. Turn the sprinklers on. When your sprinklers have filled the cans to a 1" depth, you will know how long your system takes to get the correct amount of water out. Every sprinkler system is different so this is the only way to find your particular output.
However, with heavy clay soils there could still be runoff. The best way to correct this is to run your system in small increments for each station. This may have to be done two or three times. By waiting between cycles the water has a chance to soak in. For example, if you have 6 stations in your landscape you could set them to each run for 5 minutes. By the time the last station has run, the turf around the first station has had time to soak up the water. You would then start the process over again. Depending on your particular landscape, each station could run for 5 to 10 minutes. If you have already determined how long it takes for a 1" depth, you will know how long to run each station and how many times to cycle them.