By [NXY19] the non-archimedean SYZ fibration $\rho_{\mathscr{X}_{ijk}}:S^{\an}\rightarrow\Sk(\mathscr{X}_{ijk})=\Sk(X)\simeq\mathbb{S}^{2}$ is an affinoid torus fibration (at least) away from the vertices of the triangulation of $\Sk(X)$ induced by the special fiber of $\mathscr{X}_{ijk}$, i.e. away from the $v_{D_{m}}$’s.
By Theorem B, $\rho_{\mathscr{X}_{ijk}}$ is an affinoid torus fibration over $\Star(\tau_{D_{h}})$ for $h\neq i,j,k$, as $D_{h}\simeq\mathbb{P}^{2}$ and $g_{ijk}$ is an isomorphism on the strict transform of $D_{h}$. Moreover, by Remark 3.1.7 and Eq. 3.3.1 the integral affine structure induced by $\rho_{\mathscr{X}_{ijk}}$ does not extend to $v_{D_{i}}$, $v_{D_{j}}$ and $v_{D_{k}}$.

We conclude that the singular points of the affine structure on $\Sk(X)$ induced by $\rho_{\mathscr{X}_{ijk}}$ are precisely $v_{D_{i}}$, $v_{D_{j}}$ and $v_{D_{k}}$. Corollary 3.1.6 establishes that the monodromies around these vertices are