The JAGB method has been proposed over the last years as a possible distance indicator for the galaxies in the Local Group and possibly beyond. The nature of the stars populating the J region, as also the conditions on the star formation history and on the structural properties of the galaxies for the straight application of this method need still to be investigated. We studied the populations of the J region of the colour-magnitude (J-K,J) plane of the Large and Small Magellanic Cloud (LMC and SMC, respectively), to relate the shape of the J luminosity function (JLF) to the details of the formation histories of the two galaxies, in the attempt of distinguishing the general aspects of the JLF to those more sensitive to the stellar population of the specific galaxy considered. We used a population synthesis approach, based on the combined results from stellar evolution and dust formation modelling, to find the expected distribution of the stars within the J region, and compare it with that derived from the observations of LMC and SMC stars. Some physical assumptions, mostly related to the modelling of the red giant branch and asymptotic giant branch phases of stars, are tuned, until satisfactory agreement between the expectations from synthetic modelling and the observational evidence is reached. The sources observed within the J region are identified with stars that have recently reached the C-star stage, and have not yet accumulated the extremely large amounts of carbon required to make the evolutionary track to evolve off the J region. Generally speaking, 2-3M_{sun}_ stars stay longer within the J region, while lower mass objects evolve there for at most a couple of inter-pulse phases. The analysis of the JLF of the LMC, peaked at the J magnitudes expected for these stars, confirm this understanding. In the SMC the distribution of the J fluxes is shifted to higher J magnitudes when compared to the LMC, which we interpret as the signature of an average older population, with smaller mass progenitors.