Recent studies on seismological data indicate that earthquake magnitude scales with either the dominant period or the peak amplitude in the seismogram’s first few seconds. At first sight, this may indicate that the earthquake’s final size is somehow related to the way rupture starts. One working hypothesis is that strong radiation from the initial phase of rupture is indicative of a triggering asperity releasing a consistent amount of elastic energy, with the potential to drive the fracture to large extents. We tested this concept with a number of numerical simulations, but within the models investigated, scaling was found only for ruptures extending up to about four times the size of the initial asperity; at larger distances the correlation was lost. Alternatively, a careful kinematic analysis of the earthquake source radiation shows that the initial signal recorded at any station does not necessarily correspond to the rupture initiation but may represent an extended portion of the radiating source. Using the concept of isochrones, we show that the apparent scaling may be explained by a simple kinematic model respecting causality, up to a given magnitude threshold where the scaling relation saturates. The saturation level is in agreement with that observed in some, but not all, of the real seismicity catalogs.