The S-H bond tunneling predissociation dynamics of thiophenol and its ortho-substituted derivatives (2-fluorothiophenol, 2-methoxythiophenol, and 2-chlorothiphenol) in S1 (ππ*) where the H atom tunneling is mediated by the nearby S2 (πσ*) state (which is repulsive along the S-H bond extension coordinate) have been investigated in a state-specific way using the picosecond time-resolved pump-probe spectroscopy for the jet-cooled molecules. The effects of the specific vibrational mode excitations and the SH/SD substitutions on the S-H(D) bond rupture tunneling dynamics have been interrogated, giving deep insights into the multidimensional aspects of the S1/S2 conical intersection, which also shapes the underlying adiabatic tunneling potential energy surfaces (PESs). The semiclassical tunneling rate calculations based on the Wentzel-Kramers-Brillouin (WKB) approximation or Zhu-Nakamura (ZN) theory have been carried out based on the ab initio PESs calculated in the (one, two, or three) reduced dimensions to be compared with the experiment. Though the quantitative experimental results could not be reproduced satisfactorily by the present calculations, the qualitative trends among different molecules in terms of the behavior of the tunneling rate versus the (adiabatic) barrier height or the number of PES dimensions could be rationalized. Most interestingly, the H/D kinetic isotope effect observed in the tunneling rate could be much better explained by the ZN theory compared to the WKB approximation, indicating that the nonadiabatic coupling matrix elements should be invoked for understanding the tunneling dynamics taking place in the proximity of the conical intersection.