Ask Mr. Smarty Plants

This is one of the reasons that the Lady Bird Johnson Wildflower Center talks so much about plants native not only to North America but to the areas in which those plants evolved. If your plants are not native to Central Texas, they are reacting to soils to which they are not accustomed.

From a previous Mr. Smarty Plants answer on chlorosis:

Yellowish leaves could indicate chlorosis, or lack of iron being taken up by the plant from the soil. This is often caused  by poor drainage and/or dense clay soil, which causes water to stand on the roots. Again, this could  be a problem caused by planting, perhaps without any organic material added to hole, or damage to the tiny rootlets that take up water and trace elements, including iron, from the soil.

Please read this article from the University of Illinois Extension on chlorosis. Note the comment that the presence of chlorosis is often due to high alkalinity in the soil. You can be pretty sure that your soil is alkaline, but plants native to this area are accustomed to that soil, and should be happy with it.

Among the steps we would recommend are to use some sort of iron supplement, not too much, as native plants do not ordinarily care for fertilizer. Water less, because it's possible the main problem is lack of drainage in soil where the plants are growing. Watering once a week should be adequate.  Finally, using a good quality organic mulch, spread the mulch over the root area without allowing it to touch the trunk area. This will protect the roots from heat and cold and, as the mulch decomposes, will add some material to the soil to assist in drainage.

From Texas A & M AgriLIFE Extension, please read this article on The Real Dirt on Austin Soils. If you would like to get a professional soil test packet, go to this site for forms and information.