With the development of the unified theory of coherence and polarization, the novel physical properties generated by different correlation structures of vector partially coherent beams (PCBs) have attracted much attention. Recently, a new class of structured beams have been proposed [Opt. Lett.45, 3824 (2020)10.1364/OL.397316], called vector specific non-uniformly correlated beams. These beams combine non-uniform polarization and non-uniform correlation, and they exhibit propagation features not seen in conventional vector PCBs. In this Letter, we continue the analysis of the previous work, taking radially polarized Hermite non-uniformly correlated (RPHNUC) beams as an example, and focus on the physical interpretation of the peculiar propagation features of such beams. We verify the predicted behavior of RPHNUC beams through experiment.