Now, I don't know anything about neuroscience or brain development, but hopefully I can explain the statistics in a way useful to you.

Imagine there are two groups A and B. One group, A, has slower reactions on average and high average activity The other, Group B, has higher reactions and lower than the Group A's activity. Yet inside both groups the general trend is that if someone is slower than the average reaction of their group then they're also below the average activity for their group.

If we look at the overall means without distinguishing groups, slower reaction is correlated positively with higher activity (kids from group A have higher activity and slower reaction in general, which pushes the correlation upwards. As long as the relationship in Group B isn't too strong the upward trend from Group A can easily dominate overall correlation) but inside each group the trend is actually the opposite.

This applies pretty much every time you're comparing samples. If I understood your quote correctly, they're studying a child's reaction time vs activity level by comparing the same kid in different times. The same logic applies, a person can exhibit the opposite trend to the populational average due to the same mechanism above. This can be even more dramatic, because once you start looking at averages you start losing time dependency information.

More broadly (and more formally), multivariate covariance splits in within-group and between-group terms, so if the signs of the terms are different the magnitude of one can dominate the overall sum and flip the sign.