Abstract: Tensorial non-standard neutrino interactions are studied through a combined analysis of nuclear structure calculations and a sensitivity chi(2)-type of neutrino events expected to be measured at the COHERENT experiment, recently planned to operate at the Spallation Neutron Source (Oak Ridge). Potential sizeable predictions on transition neutrino magnetic moments and other electromagnetic parameters, such as neutrino milli-charges, are also addressed. The non-standard neutrino-nucleus processes, explored from nuclear physics perspectives within the context of quasi-particle random phase approximation, are exploited in order to estimate the expected number of events originating from vector and tensor exotic interactions for the case of reactor neutrinos, studied with TEXONO and GEMMA neutrino detectors.