In the proof of Proposition 4.3, we have constructed a dlt pair $(\mathscr{Y},\mathscr{Y}_{s})$ with $\mathscr{Y}$ of finite type over $k$ such that there exists an isomorphism of $k$-schemes $\mathscr{X}_{k}\to\mathscr{Y}_{s}$ that identifies the log canonical centers of $(\mathscr{X},\mathscr{X}_{k})$ contained in $\mathscr{X}_{k}$ with those of $(\mathscr{Y},\mathscr{Y}_{s})$ contained in $\mathscr{Y}_{s}$. Thus the result follows from the corresponding properties of $(\mathscr{Y},\mathscr{Y}_{s})$ proven in [Ko13, 4.16]. ∎