The propagation of magnons along a symmetry path may depend on the direction of propagation, similar to many other quasiparticles in nature. This phenomenon is commonly referred to as nonreciprocity. In addition to the fact that it is of great interest to understand the fundamental physical mechanism leading to this nonreciprocal propagation, the phenomenon of magnon nonreciprocity may be used to design magnon-based logic devices. Recently, it has been demonstrated that a significantly large spin-orbit coupling can lead to giant nonreciprocity of exchange-dominated terahertz magnons, when they are excited by means of spin-polarized electrons [Phys. Rev. Lett. 132, 126702 (2024)]. Here, by providing experimental results on two additional systems we demonstrate the generality of the observed phenomenon. Comparing the results of a Co/Ni bilayer on Ir(001) to those of a Co double layer on Ir(001) and W(110), we unravel the impact of the interfacial electronic hybridization on the observed phenomenon and provide further insights into the microscopic mechanism leading to this nonreciprocal magnon excitation. It was observed that the interfacial electronic hybridization is of some importance but is not crucial for the magnon nonreciprocity. This is an important observation since the electronic hybridization is known to be a key aspect in the determination of the magnetic properties at the interface. On the other hand, the choice of the incident energy of the incoming electron beam is decisive for the observation of the effect. Our results indicate that depending on the energy of the incident electron beam and the scattering geometry the magnon nonreciprocity can be tuned and even be inverted for some ranges of the magnon momentum. The results may inspire new ideas for the generation of nonreciprocal ultrafast terahertz magnons in ultrathin films of 3d magnetic metals as well as in two-dimensional van der Waals magnets, interfaced with solids possessing a large spin-orbit coupling, for applications in the field of magnonics.