Actually, using only the peak (beta) doesn't change the results. Some correlations are consistent, while some others (the majority) are not. Tried with R^2 values too (squared and eventually inverted): nothing.
It's frustrating.

I understand that these are two distinct, and not commutative, processes, but the statistically significant effect of the covariate (reaction time) should indicate high level of confidence for the correlation; otherwise, I don't see the meaning of using the model.

I was wondering if this situation can also imply the reverse problem (misdetection of true effects), and effectively it seems to be the case: for the seed in which I still see correlations after the averaging, in overthreshold clusters (0.05 < alpha < 0.10, for example) there is a significant correlation.

I'm puzzled!