The multi-tier GW+EDMFT scheme is an ab-initio method for calculating the electronic structure of correlated materials. While the approach is free from ad-hoc parameters, it requires a selection of appropriate energy windows for describing low-energy and strongly correlated physics. In this study, we test the consistency of the multi-tier description by considering different low-energy windows for a series of cubic SrXO3 (X = V, Cr, Mn) perovskites. Specifically, we compare the 3-orbital t2g model, the 5-orbital t2g + eg model, the 12-orbital t2g + Op model, and (in the case of SrVO3) the 14-orbital t2g + eg + Op model and compare the results to available photoemission and X-ray absorption measurements. The multi-tier method yields consistent results for the t2g and t2g + eg low-energy windows, while the models with Op states produce stronger correlation effects and mostly agree well with experiment, especially in the unoccupied part of the spectrum. We also discuss the consistency between the fermionic and bosonic spectral functions and the physical origin of satellite features, and present momentum-resolved charge susceptibilities.