In a swirl-stabilised liquid fuel burner, the fuel spray response to the Precessing Vortex Core (PVC) and air flow rate modulations is analysed in non-reacting conditions. A siren-like device is used to modulate the air flow rate at a frequency corresponding to longitudinal combustion instability oscillations observed during reacting tests. Time-resolved Mie scattering images of the fuel spray are recorded and treated with multiple post-processing methods based on Dynamic Mode Decomposition. The spray velocity fluctuations induced by the PVC and the siren-generated modulations are extracted from noisy datasets and studied. The evolution of the PVC impact on the spray for different levels of flow rate fluctuations is followed and a nonlinear interaction mode is highlighted for several intensities of flow rate modulations. It is shown that increasing the flow rate modulations tend to weaken the PVC impact on the spray, progressively disturbing its structure, starting from the downstream part and progressing upstream. These observations on the fuel spray can be used to understand and interpret data obtained in reacting conditions, for example when competition between PVC and longitudinal combustion instabilities occurs.