Bounded Twin-Width Tournaments are $\dchi$-Bounded

For a tournament $T$ and a vertex ordering $\prec$, let $T^{\prec}$ be the graph of backward arcs in $\prec$. The diclique number of a tournament is $\domega(T)=\min_{\prec}ω(T^{\prec})$, and the dichromatic number is $\dchi(T)=\min_{\prec}χ(T^{\prec})$. We prove a mixed parameter transfer theorem: