Ask Mr. Smarty Plants

Pull it out.

Sorry to not have an easier suggestion, but at least it is not bermudagrass. The St. Augustine species is vigorous and spreads rapidly by creeping stolons. Its requirements, other than mild winters, include moist and somewhat fertile soil. It is not as drought tolerant or as cold tolerant as bermudagrass so its inland movement has been restricted to states and countries bordering on coastal zones. Left out in the sun with no water, it will brown and sicken, but you are very kindly providing it with moist, fertile soil and no competition. You can't spray it with a herbicide, because you are trying to raise more desirable plants in the same area. Even spraying with a grass-specific herbicide would likely also take down the zoysia grass. From personal experience, we can tell you that St. Augustine is not particularly bothered by mulch, it's nice and shady and cool and damp under there. Eventually, a stolon will have to pop up for some sunlight, and you need to nab it then, and get as much of it out as possible. And keep doing it.

Now for a word from our sponsor. The Lady Bird Johnson Wildflower Center is dedicated to use, propagation and protection of plants native to North America and to the area in which they are being grown. All three of the grasses mentioned in the paragraph above are non-native to North America.

From Texas Cooperative Extension, authored by Richard L. Duble: Zoysia, the grass you planted, is a sod-forming, slow-growing perennial with both stolons and rhizomes. It grows from early Spring to late Fall when moisture and nutrient requirements are met. It is native to China, Japan and other parts of Southeast Asia. 

Again from Texas Cooperative Extension, by Richard L. Duble: St. Augustine is native to the West Indies and Africa. It is a coarse-textured stoloniferous species that roots at the nodes. It requires quite a lot of water and can be caused serious damage by several insect pests.

University of California Integrated Pest Management: Pests in Gardens and Landscapes-Bermudagrass: This grass for turf and cattle feed was introduced into this country during Colonial times from Africa or India. With both stolons and rhizomes, it can advance aggressively and virtually climb ornamentals to reach sunshine. It is a particularly noxious weed throughout the South. 

Next time you need to plant grass, consider the natives. Visit our Native Plant Database, and use Narrow Your Search to find grasses native to Texas and suitable to grow in Austin.