Functionalizing single-walled carbon nanotubes (SWNTs) with light-harvesting molecules is a facile way to construct donor-acceptor nanoarchitectures with intriguing optoelectronic properties. Magnesium-centered bacteriochlorin (MgBC), chlorin (MgC), and porphyrin (MgP) are a series of tetrapyrrole macrocycles comprising a central metal and four coordinated aromatic or antiaromatic five-membered rings linked by methine units, which show excellent visible light absorption. To delineate the effects of the aromaticity of coordinated rings on the optoelectronic properties of the nanocomposites, the photoinduced energy and charge transfer dynamics between Mg-centered tetrapyrroles and SWNTs are explored. The results show that excited energy transfer (EET) can occur within MgP@SWNT ascribed to the stabilization of the highest occupied molecular orbital (HOMO) in MgP with the increase of aromatic coordinated rings, while only electron transfer can take place in MgBC@SWNT and MgC@SWNT. Non-adiabatic dynamics simulations demonstrate that electron and hole transfer from MgP to SWNT is asynchronous. The electron transfer is ultrafast with a timescale of ca. 50 fs. By contrast, the hole transfer is significantly suppressed, although it can be accelerated to some extent when using a lower excitation energy of 2.2 eV as opposed to 3.1 eV. Further analysis reveals that the large energy gaps between charge-donor and charge-acceptor states play a crucial role in regulating photoexcited state relaxation dynamics. Our theoretical insights elucidate the structure-functionality interrelations between Mg-centered tetrapyrroles and SWNTs and provide a comprehensive understanding of the underlying charge transfer mechanism within MgP@SWNT nanocomposites, which paves the way for the forthcoming development of SWNT-based photo-related functional materials with targeted applications.