The focus of the present paper is to understand the large scale unsteadiness in the atomization of swirl coaxial jets and correlate it with the downstream spray statistics. A gas-centered swirl coaxial atomizer, in which a gaseous jet fragments an annular swirling liquid sheet, displays pulsating flow at certain momentum flux ratios (MFRs). These conditions were chosen to study the unsteady dynamics in the spray formation. Various zones of the spray such as near orifice region, primary atomization zone and far field spray were diagnosed using high-speed shadowgraphy technique. Proper orthogonal decomposition was employed on the time-resolved spray images to understand various unsteady modes. Three modes observed prominently were identified as large scale unsteady structures viz. axisymmetric pulsating mode, explosive mode and swirling mode. The pulsating mode was found to be more dominant in the pulsation regime, whereas the other modes gained significance at higher MFRs when the pulsation regime ceases to exist. Fourier analysis of temporal coefficients pertaining to pulsating mode showed a definitive frequency. The analysis of liquid shedding rate was found to be in synchronization with the pulsating mode which shows the upstream influence on periodic atomization. Spatio-temporal measurements of droplet sizes were carried out far from the atomizer. The temporal variation in the droplet number density and Sauter Mean Diameter depicted unsteady behavior; however, there is no preferred frequency in the power spectrum. This clearly indicates that the far field spray loses its memory of upstream periodic atomization in the pulsation regime of swirl coaxial atomizer.