In our HST photometric survey, we have been searching for multiple stellar populations (MPs) in Magellanic Clouds (MCs) massive star clusters which span a significant range of ages (similar to 1.5-11Gyr). In the previous papers of the series, we have shown that the age of the cluster represents one of the key factors in shaping the origin of the chemical anomalies. Here, we present the analysis of four additional clusters in the MCs, namely Lindsay 38, Lindsay 113, NGC 2121, and NGC 2155, for which we recently obtained new UV HST observations. These clusters are more massive than similar to 10(4) M(circle dot)and have ages between similar to 2.5 and similar to 6Gyr, i.e. located in a previously unexplored region of the cluster age/mass diagram. We found chemical anomalies, in the form of N spreads, in three out of four clusters in the sample, namely in NGC 2121, NGC 2155, and Lindsay 113. By combining data from our survey and HST photometry for three additional clusters in the Milky Way (namely 47 Tuc, M15, and NGC 2419), we show that the extent of the MPs in the form of N spread is a strong function of age, with older clusters having larger N spreads with respect to the younger ones. Hence, we confirm that cluster age plays a significant role in the onset of MPs.