  In this article we prove that Lax pairs associated with $\hbar$-dependent six
Painlev\'e equations satisfy the topological type property proposed by
Berg\`ere, Borot and Eynard for any generic choice of the monodromy parameters.
Consequently we show that one can reconstruct the formal $\hbar$-expansion of
the isomonodromic $\tau$-function and of the determinantal formulas by applying
the so-called topological recursion to the spectral curve attached to the Lax
pair in all six Painlev\'e cases. Finally we illustrate the former results with
the explicit computations of the first orders of the six $\tau$-functions.
