We consider evolutionary systems, i.e., systems of linear partial differential equations arising from the mathematical physics. For these systems, there exists a general solution theory in exponentially weighted spaces, which can be exploited in the analysis of numerical methods. The numerical method considered in this paper is a discontinuous Galerkin method in time combined with a conforming Galerkin method in space. Building on our recent paper (Franz, S., Trostorff, S. & Waurick, M. (2019) Numerical methods for changing type systems. IMAJNA, 39, 1009-1038), we improve some of the results, study the dependence of the numerical solution on the weight parameter and consider a reformulation and post-processing of its numerical solution. As a by-product, we provide error estimates for the dG-C0 method. Numerical simulations support the theoretical findings.