I have never managed to keep Texas Ranger alive through a UK winter, so don't really have any useful information. I don't use drip irrigation either because I like to hand-water and know exactly how much water each plant is receiving. For newly planted shrubs, these look quite large and mature - can be tricky getting established. I think I would be carefully monitoring the amount of irrigation, with a weekly deep watering, to ensure the entire root area has been moistened, then allowing the soil to dry between waterings. Have you done any fertilising? Leucophyllum are very sensitive to fertiliser and can easily exhibit symptoms of chlorosis if over fertilised. They grow well in my nutrient poor soil but struggle with even the minuscule amounts of winter rain in cold soil.

Hopefully, someone from your region will chime in with more relevant advice.