It follows from the definition of good dlt model $\mathscr{X}$ of $X$ that the Berkovich retraction $\rho_{\mathscr{X}}:X^{\an}\rightarrow\Sk(\mathscr{X})$ is an affinoid torus fibration over the interior of the maximal faces $\tau$ of $\Sk(\mathscr{X})$. Indeed, the retraction over $\textrm{Int}({\tau})$ only depends on the formal completion of $\mathscr{X}$ along the corresponding 0-dimensional stratum $p$. The pair $(\mathscr{X},\mathscr{X}_{k})$ is snc at $p$, hence the claim.