We present optical integral field unit (IFU) observations of two gas pillars surrounding the Galactic young massive star cluster NGC 3603. The high S/N and spectral resolution of these data have allowed us to accurately quantify the H-alpha, [NII] and [SII] emission line shapes, and we find a mixture of broad (FWHM~70-100 km/s) and narrow (10000 cm-3. In one pillar we found that these high densities are only found in the narrow component, implying it must originate from deeper within the pillar than the broad component. From this, together with our kinematical data, we conclude that the narrow component traces a photoevaporation flow, and that the TML forms at the interface with the hot wind. On the pillar surfaces we find a consistent offset in radial velocity between the narrow (brighter) components of H-alpha and [NII] of ~5-8 km/s, for which we were unable to find a satisfactory explanation. We urge the theoretical community to simulate mechanical and radiative cloud interactions in more detail to address the many unanswered questions raised by this study. ; Comment: 17 pages, 19 figures, accepted to MNRAS