  Starting from a $d\times d$ rational Lax pair system of the form $\hbar
\partial_x \Psi= L\Psi$ and $\hbar \partial_t \Psi=R\Psi$ we prove that, under
certain assumptions (genus $0$ spectral curve and additional conditions on $R$
and $L$), the system satisfies the "topological type property". A consequence
is that the formal $\hbar$-WKB expansion of its determinantal correlators,
satisfy the topological recursion. This applies in particular to all $(p,q)$
minimal models reductions of the KP hierarchy, or to the six Painlev\'e
systems.
