The interpretation of experimental and numerical data describing off-equilibrium aging dynamics crucially depends on the connection between spontaneous and induced fluctuations. The hypothesis that linear response fluctuations are statistically subordinated to irreversible outbursts of energy, so-called quakes, leads to predictions for the average values and the fluctuation spectra of physical observables in reasonable agreement with experimental results (see e.g. Sibani et al 2006 Phys. Rev. B 74 224407). Using simulational data from a simple but representative Ising model with plaquette interactions, direct statistical evidence supporting the subordination hypothesis is presented and discussed in this work. Both energy and magnetic fluctuations are analyzed, with and without an external magnetic field present. In all cases, fluctuation spectra have a Gaussian zero centered component. For large negative values, the energy spectrum additionally features an intermittent tail describing the quakes. In the magnetization spectrum, two intermittent tails are present. These are symmetric around zero for zero-field, but asymmetric in other cases. The field has thus a biasing effect on the spontaneous intermittent magnetic fluctuations. Furthermore, the field has a negligible effect on the energy fluctuation spectra. From the observed strict temporal correlation between quakes and intermittent magnetization fluctuations, it is possible to conclude that the linear response is controlled by the quakes and inherits their temporal statistics. On this basis, the information culled from intermittent linear response data can be analyzed in the same way as spontaneous thermal energy fluctuations. The latter have a central rôle in thermally activated dynamics, but are harder to measure than linear response data.