  Let $F_n(\Sigma_{g,1})$ denote the configuration space of $n$ ordered points
on the surface $\Sigma_{g,1}$ and let $\Gamma_{g,1}$ denote the mapping class
group of $\Sigma_{g,1}$. We prove that the action of $\Gamma_{g,1}$ on
$H_i(F_n(\Sigma_{g,1});\mathbb{Z})$ is trivial when restricted to the $i^{th}$
stage of the Johnson filtration $\mathcal{J}(i)\subset \Gamma_{g,1}$. We give
examples showing that $\mathcal{J}(2)$ acts nontrivially on
$H_3(F_3(\Sigma_{g,1}))$ for $g\ge 2$, and provide two new conceptual
reinterpretations of a certain group introduced by Moriyama.
