Boreal summer intraseasonal oscillation (BSISO) is the major mode of tropical variability during the Indian summer monsoon(ISM), it controls the dry and wet spells of ISM and thus is crucial for agricultural yield in the country. Understanding the future of BSISO is essential as it has been established recently that the large-scale BSISO environment enhances the probability of extreme rainfall events (EREs) enormously. In this study, the ability of Climate Model Inter Comparison Project (CMIP6) models to capture the northward propagation of boreal summer intraseasonal oscillation (BSISO) is examined using a counting algorithm. A composite moisture budget reveals the difference in moisture dynamics between the above-average-performing (AAPM) and below-average-performing (BAPM) models, AAPM composite has a more robust horizontal moisture advection ahead of the convection centre than the BAPM composite. This difference in the horizontal moisture advection between AAPM and BAPM is mainly caused by the weaker wind and moisture perturbations in the BAPM. The BAPM composite shows a weaker equatorial convection signal compared to the AAPM composite, resulting in weaker wind and moisture perturbations and a lesser number of northward propagations. Finally, we understand the future of BSISO by examining the projections of Shared Socioeconomic Pathways 370 (SSP370) from the available AAPMs. The background moisture will be enhanced uniformly in the future, leading to no substantial change in gradients. The equatorial convection enhances and broadens in the future projections, leading to very little change in the wind perturbations. This results in the enhancement of BSISO rainfall by 63% in the Bay of Bengal and 42% in the Arabian Sea. However, the proportion of northward propagations remains the same as moisture advection remains the same. The study implies that with a correct representation of BSISO's equatorial convection, the prediction of BSISO and extreme rainfall associated with BSISOs becomes more reliable.