Step 1: Think about what the carotid artery is sensing.
Blood in the carotid artery is the first blood to reach the brain, so it is the ideal spot to test how the brain reacts to a change in blood concentration before that blood mixes further.
Step 2: Identify the sensing cells.
Specialised nerve cells called osmoreceptors pick up small shifts in the salt concentration of this blood. These cells lie right around the supraoptic nucleus of the hypothalamus.
Step 3: Follow the reflex.
Once the osmoreceptors near the supraoptic nucleus fire, the supraoptic neurons themselves (which manufacture ADH) change their output, and ADH travels down their axons to the posterior pituitary for release into the blood. This whole reflex is the basis of the body's water balance control, and it is switched on by a change of tonicity delivered right through the carotid artery.
Step 4: Cross off the wrong nuclei.
The medial hypothalamic nucleus governs hunger and satiety. The preoptic nucleus governs body temperature. The paraventricular nucleus also secretes ADH and oxytocin, but the osmoreceptor zone that first answers a carotid tonicity change belongs to the supraoptic nucleus.
Step 5: State the answer.
\[ \boxed{\text{Supraoptic nucleus of the hypothalamus}} \]