  In this work we study the hadron-quark phase transition matching relativistic
hadrodynamical mean-field models (in the hadronic phase) with the more updated
versions of the Polyakov-Nambu-Jona-Lasinio models (on the quark side).
Systematic comparisons are performed showing that the predicted hadronic phases
of the matching named as RMF-PNJL, are larger than the confined phase obtained
exclusively by the Polyakov quark models. This important result is due to the
effect of the nuclear force that causes more resistance of hadronic matter to
isothermal compressions. For sake of comparison, we also obtain the matchings
of the hadronic models with the MIT bag model, named as RMF-MIT, showing that
it presents always larger hadron regions, while shows smaller mixed phases than
that obtained from the RMF-PNJL ones. Thus, studies of the confinement
transition in nuclear matter, done only with quark models, still need nuclear
degrees of freedom to be more reliable in the whole $T\times\mu$ phase diagram.
