Each of the provided examples from the parent comment are causal perturbations to the system that establish necessity (although perhaps not sufficiency) beyond a pure correlation. If you lesion a part of the brain, you lose associated "mental" faculties. If you perturb the system via disease or chemicals, you observe a corresponding change in the mental state. This is evidence of a one way interaction beyond correlation.
You appear to be saying that non-mental event A temporally precedes mental event B, therefore the non-mental must be the cause of the mental, rather than the mental being the cause of the non-mental.
However, "you perturb the system via disease or chemicals" is not non-mental. There is a mental act of will to do perform such a perturbation, and a mental awareness of such perturbation being performed.
We observe many correlations between the neurological and the mental, and it seems likely that in the years and decades to come we will learn many more. Materialists argue that this is evidence that the mental is a product of the neurological. But what about the idealist alternative, that the neurological is a product of the mental? An observed correlation between two phenomena cannot, by itself, tell us which of the two is more fundamental.