I can't imagine a less suitable plant for a desert planting! It will always require regular routine irrigation to survive and your alkaline soil and water conditions will not be to its liking, hence the chlorosis. And time will have no bearing on sun tolerance, either. I'd be highly inclined to cut my losses and replant with something more appropriate to your location and climate. Rather than plant shopping at a box store - always a risk for hardiness/suitability - visit a better retail garden center in your area and see what they suggest. Evergreen drought tolerance would top my list of requirements. Off the top of my head, oleander, hopbush (Dodonaea viscosa) or Arizona rosewood (Vauqualinia californica) come to mind but upright juniper or Italian cypress could work also. But forget the photinia - a very poor choice for your situation.

I've found dry potting soil rootballs years after planting. The finer textured natural soil around them had a greater attraction for water, so as long as the original potting soil rootball hadn't decomposed enough to lose its coarse texture it continued to lose water to the surrounding soil. Healthy, vigorous plants survive this and grow when watered frequently enough after planting to compensate, and when planted directly into native soil or topsoil so that as soon as they root into it they are tapping into the moisture the latter contains. Liberal amending of planting hole backfill or replacing backfill with potting soil, planting mix or other coarse material (pit planting) creates a larger area prone to drying and which the roots have to cross to get into the soil beyond. On a damp, heavy soil a planting hole backfilled with coarser material, including a lighter natural soil or topsoil mix may act as a sump. Perhaps the optimum when planting hardy stock, not prone to freezing during winter in the local climate is planting during fall and washing the potting soil or field soil off, spreading the roots out without cutting them. Undamaged roots planted early enough in fall may then elongate considerably and immediately establish the new plant. Most elongation (more than half the annual total) occurs in fall after the overwintering terminal buds are set on the branches.

A big, bold architectural plant that is is mostly evergreen in my climate. Has a deep tap root and once sited, it's pretty much there for the duration :-)) Prefers a moist, rich soil in more sun that shade, It's quite drought tolerant once established but can go semi-dormant in midsummer if sited in too much sun. If the leaves start looking yellowish and crispy, just cut it back and it will produce a new rosette of foliage. It is sometimes difficult to establish. I also find it less of a spreader or thug than some of its cousin species although a happy clump will get large over time. Stunning summer flower spikes up to 5-6' tall are attractive to hummingbirds. Check locally for sure, but I doubt this plant is sufficiently hardy to survive a zone 5 winter.....usually listed only to zone 7.

@rhizo so that fact sheet did not come out and say the neonicotinoids are not recommended. The exact words are: "Neonicotinoids vary in effectiveness for thrips control. For example, dinotefuran (Safari), available to professional applicators, can provide good control of thrips. Imidacloprid (Bayer Advanced Tree & Shrub Insect Control, Merit) commonly fails to provide satisfactory thrips control, and imidacloprid generally is not recommended for thrips." What is clear from that page is that you want to wait until the plant stops flowering, otherwise you are poisoning pollinators like bees. That's an important message. The alternatives are problematic. * Using neem oil on a large hedge requires a professional to apply thoroughly and spray evenly. That ends up costing me $400/year for two site visits. That's painful. * Using beneficial insects is the way I want to go eventually, but to do this I need to know the exact species of thrip. I will have to wait for July when their population rises to make that identification, and for the Summer months I can try to use predator insects. That will be another $100 at minimum, and there is scant proof that approach works for a small garden hedge.