We update the study of the production of direct J/Psi in association with a Z boson at the Next-to-Leading Order (NLO) in alpha_s by evaluating both the yield differential in P_T and the J/Psi polarisation in the QCD-based Colour-Singlet Model (CSM). Contrary to an earlier claim, QCD corrections at small and mid P_T are small if one assumes that the factorisation and the renormalisation scales are commensurate with the Z boson mass. As it can be anticipated, the t-channel gluon-exchange (t-CGE) topologies start to be dominant only for P_T > mZ/2. The polarisation pattern is not altered by the QCD corrections. This is thus far the first quarkonium-production process where this is observed in the CSM. Along the same lines, our predictions for direct Upsilon+Z are also given.