Summer is a stressful time to establish plants in the south. The key is to keep the soil moist but not soggy wet at both extremes of soil moisture will be very detrimental to the plants. I think if you can dig down a few inches to feel the soil around the root ball and water accordingly that will be the best guide at least until they have a year to really get better established.
Since the brown area is on one side I wonder if it could be due to some other cause...sunburn, damage from a spray of some sort, etc.? Nevertheless, your best bet is to keep the soil moist and give them time. With fall coming they should be able to get better established with less stress and then come out fine next spring.
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