The morphism $\mathscr{Z}\rightarrow\mathscr{X}_{ijk}$ is the blow-up of the 24 exceptional curves of $g_{ijk}$. In particular, the exceptional divisor $E_{q}$ is the preimage in $\mathscr{Z}$ of a curve contained in $\tilde{D}_{l}$; it follows that $v_{E_{q}}(\tilde{z}_{l})=1$ and $v_{E_{q}}(\tilde{z}_{h})=0$, where $\tilde{z}_{l},\tilde{z}_{h}$ are local equations for $\tilde{D}_{l},\tilde{D}_{h}$ on $\mathscr{X}_{ijk}$. The Berkovich retraction $\rho_{\mathscr{X}_{ijk}}$ is linear on $W_{q}$ and hence depends only on the image of $v_{q}$, which is determined by $v_{E_{q}}(\tilde{z}_{l})$ and $v_{E_{q}}(\tilde{z}_{h})$. Thus we conclude that $\rho_{\mathscr{X}_{ijk}}(v_{q})=v_{l}$ and we have the result. ∎