A modeling study has been carried out to understand the similarities and differences in the genesis sequence of a Bay of Bengal tropical cyclone Madi (6-13 December 2013) and the Atlantic Ocean tropical cyclone Florence (3-12 September 2006) on the applicability of hypotheses of the marsupial theory of tropical cyclogenesis. We examined the role of the protective pouch and warm core formation during their genesis and intensification phases. We have chosen tropical cyclone Madi and tropical cyclone Florence for our study specifically due to both of these tropical cyclones originated from westward moving parent disturbance embedded in the intertropical convergence zone. Also, the genesis and intensification of tropical cyclone Florence were accompanied by a series of Saharan dust outbreaks. Our results indicated that the dry air intrusion was not a dominant detrimental factor for the genesis of tropical cyclone Madi and showed rapid intensification within the pouch region. However, in the case of the tropical cyclone Florence, the delay in the intensification as a category 1 tropical cyclone from its tropical depression stage was due to entrainment of the dry air into the core of cyclonic vortex up to 700 hPa from above. The results from this study showed that the wave pouch played a most significant role in the vorticity upscale cascade (First hypothesis) and moisture aggregation (Second hypothesis) in pregenesis period of both the tropical cyclones. It also prevented the lateral dry air intrusion (Second hypothesis) from the Saharan Air Layer during the genesis phase of tropical cyclone Florence.