An attempt to unfold the respective influence of the fusion and fission stages on typical fission observables, and namely the neutron pre-scission multiplicity, is proposed. A four-dimensional dynamical stochastic Langevin model is used to calculate the decay by fission of excited compound nuclei produced in a wide set of heavy-ion collisions. The comparison of the results from such a calculation and experimental data is discussed, guided by predictions of the dynamical deterministic HICOL code for the compound-nucleus formation time. While the dependence of the latter on the entrance-channel properties can straigthforwardly explain some observations, a complex interplay between the various parameters of the reaction can occur in other cases. A multi-dimensional analysis of the respective role of these parameters, including entrance-channel asymmetry, bombarding energy, compound-nucleus fissility, angular momentum and excitation energy, is proposed. It is shown that, depending on the size of the system, apparent unconsistencies may be deduced when projecting onto specific ordering parameters. The work suggests the possibility of delicate compensation effects in governing the measured fission observables, thereby highlighting the necessity of a multi-dimensional discussion.