A drought-tolerant plant survives on limited water because its roots are deep enough to find what is down there, or because it is built to lose less. Neither of those is true on the day it comes out of the pot. A nursery plant has a shallow root ball that has been watered daily its whole life, and it has no more drought tolerance at that moment than a lettuce.
It takes about two full growing seasons of regular watering for a plant to earn the label on its own tag. That is the single most misunderstood thing about xeric planting, and it is why so many water-wise landscapes fail in their first summer. Somebody plants a bed of drought-tolerant material in June, waters it like the label says, and loses most of it by August — not because the plants were wrong, but because they were asked to do something their roots could not do yet.
The other half is less obvious: established drought-tolerant plants are frequently killed by too much water rather than too little. A plant adapted to dry ground and put on a lawn irrigation schedule in heavy soil sits wet, rots, and dies looking overwatered — yellowing, soft, collapsing. In a mixed planting this is common, because the xeric shrubs end up on the same zone as everything else.
It is also worth knowing that some drought-tolerant plants go summer-dormant. They stop, look tired or half-dead in the worst heat, and come back when it breaks. That is the strategy working, not the plant failing, and it is worth knowing which of yours do it before you pull one out in August.
