Non-standard coherent neutrino scattering off nuclei is extensively studied through realistic nuclear structure calculations performed within the framework of the quasi-particle random phase approximation (QRPA). More specifically, we focus on the accurate estimation of the number of events expected to be measured by the COHERENT experiment at the Spallation Neutron Source at Oak Ridge, as well as by the reactor neutrino experiments TEXONO and GEMMA. To this purpose our study concentrates on the relevant detector materials 20 Ne, 40 Ar, 76 Ge and 132 Xe. In this context, we obtain stringent constraints on the vector and tensor non-standard interaction parameters and examine their impact on various electromagnetic neutrino phenomena such as neutrino magnetic moments and neutrino milli-charges. Our results indicate that the aforementioned experiments offer significant prospects to probe neutrino properties predicted in theories beyond the Standard Model.