But the minor premise is saying he didn’t get a migraine.
P is not saying that the only way he gets migraines is from eating nightshades, so the conclusion is false in general, though it might be right in his case.
The conclusion is that he did not eat nightshades. If eating nightshades is supposed to give him headaches and he doesn’t have a headache, then he must have not eaten nightshades.
Now, I realize that logic paints things in a very black and white manner, and I don’t think real life works that way. Therefore, I can see how the conclusion drawn above may, in some cases, be false. When he says “If I eat nightshades, then I get migraines,” he might mean nightshades usually give him migraines or that 99% of the time they do, or perhaps on occasion nightshades give him minor headaches which he doesn’t consider strong enough to be migraines. If that’s the case, then sure it’s possible for him to eat nightshades and not get migraines, but he certainly said, in the minor premise, that he didn’t get a migraine.