In this study, we use first-principles calculations to investigate the geometry, the electronic and the magnetic structure as well as to propose the laser-induced ultrafast spin dynamics on the tubular FeB₂₀ and Fe₂B₂₀ clusters. Our results show that the FeB₂₀ is a stable configuration when its Fe atom gets preferably adsorbed inside the B₂₀ tube, while the Fe₂B₂₀ is more stable configuration when one of its two Fe atoms is located inside and the other outside the boron tube. In the latter cluster, due to the higher number of d states introduced by the additional magnetic atom, the density-of-states in the low-energy region becomes higher, thus leading to richer spin dynamics. The different local geometries of the two Fe atoms lead to a multitude of many-body states with high degree of spin-density localization. Based on the calculated ground state and excited states and by using suitably tailored laser pulses we achieve ultrafast spin-flip and spin crossover scenarios for both structures. Besides, the spin-flips reach a high fidelity (above 89.7%) and are reversible, while the crossovers have lower fidelity (below 78%) and are irreversible. We also propose an ultrafast spin-transfer process from Fe2 to Fe1 for Fe₂B₂₀. The present investigation, in which we predict various ultrafast spin dynamic taken by magnetic atoms absorbed inside and outside of tubular boron clusters, is expected to provide significant theoretical guidance for the future experimental implementation and the potential applications of the relevant spin logic functional devices.