You might leave the sprinkler system out of it, but duplicate its flow by opening all the faucets on sinks and bathtubs, and if you aren't seeing brown water by then, open some outdoor hose bibs.
Talk to the water department, and see if they have a schedule of flushing the mains, which gets rid of sediment in the system.
I see, you are suggesting that maybe there is sediment in the main water system and only the sprinkler system is active enough to aggitate the existing sediment?
Thanks.