We study the Cold Nuclear Matter (CNM) effects on J/Psi and Upsilon production, whose understanding is fundamental to evaluate the Quark Gluon Plasma or Hot Nuclear Matter Effects. Two CNM effects are of particular importance: the modifications (here, shadowing) of the initial parton distributions (PDF) and the nuclear absorption the \bar{c}c (or \bar{b}b)-pair. Recent theoretical works have emphasized that the J/Psi production at low and mid-pT proceed via a 2 -> 2 process instead of a 2 -> 1 process, as assumed in the usual studies of CNM effects. When taking into account the exact kinematics of the 2 -> 2 process, visible differences appear in the obtained shadowing corrections, irrespective of which shadowing parametrization is used. This naturally induces changes in the absorption cross-section fit to the data, and hence to the deduced rapidity dependence. We will present our results in dA and AA collisions at RHIC and LHC energies, using several parametrizations of the nuclear PDF, and including the pT-dependence of CNM effects up to mid-values of pT, which are not accessible with the usual simplified kinematics. We extend our study to the upsilon case, where the first experimental results in dA at RHIC energy are available.