We study macroscopic observables of large random matrices introduced by Pennington and Worah, of the form

, where W and X are random rectangular matrices with independent entries and h is a function evaluated entry-wise. We allow the variance of the entries of the matrices to vary from entry to entry. We complement Péché perspective from [Electron. Commun. Probab. 24 (2019), no. 66, 1-7] showing a decomposition of Y (h) whose and traffic asymptotic traffic-equivalent for their ingredients, when h belong to the space of odd polynomials. This give a new interpretation of the "linear plus chaos" phenomenon observed for these matrices.