Nuclear spin driven quantum tunneling of magnetization (QTM) phenomena, which arise from admixture of more than two orthogonal electronic spin wave functions through the couplings with those of the nuclear spins, are one of the important magnetic relaxation processes in lanthanide single molecule magnets (SMMs) in the low temperature range. Although recent experimental studies have indicated that the presence of the intramolecular f-f interactions affects their magnetic relaxation processes, little attention has been given to their mechanisms and, to the best of our knowledge, no rational theoretical models have been proposed for the interpretations of how the nuclear spin driven QTMs are influenced by the f-f interactions. Since quadruple-decker phthalocyanine complexes with two terbium or dysprosium ions as the magnetic centers show moderate f-f interactions, these are appropriate to investigate the influence of the if interactions on the dynamic magnetic relaxation processes. In the present paper, a theoretical model including ligand field (LF) potentials, hyperfine, nuclear quadrupole, magnetic dipolar, and the Zeeman interactions has been constructed to understand the roles of the nuclear spins for the QTM processes, and the resultant Zeeman plots are obtained. The ac susceptibility measurements of the magnetically diluted quadruple-decker monoterbium and diterbium phthalocyanine complexes, [Tb-Y] and [Tb-Tb], have indicated that the presence of the f-f interactions suppresses the QTMs in the absence of the external magnetic field (H-dc) being consistent with previous reports. On. the contrary, the faster magnetic relaxation processes are observed for [Tb-Tb] than [Tb-Y] at H-dc = 1000 Oe, clearly demonstrating that the QTMs are rather enhanced in the presence of the external magnetic field. Based on the calculated Zeeman diagrams, these observations can be attributed to the enhanced nuclear spin driven QTMs for [Tb-Tb]. At the H-dc higher than 2000 Oe, the magnetic relaxations become faster with increasing H-dc for both complexes, which are possibly ascribed to the enhanced direct processes. The results on the dysprosium complexes are also discussed as the example of a Kramers system.