As far as I know, the only native summer-run on Puget Sound streams is the Deer Creek summer-run on the North Fork Stilly. All remaining summer-runs on Puget Sound streams are of hatchery origin and they don't seem to reproduce well.

With this said, hatchery summer run wander to great lengths over the many months between entering the river and spawning. I've heard of Skykomish summer-run caught in the Snoqualmie; North Fork Stilly summer-run caught in the South Fork. Come the first rains during the fall, though, they bolt back to where they were planted. Tributary streams, especially if there in good shape (limited development, logging, etc.) can run cooler during the summer providing refuge from those August/September high temperatures.