The 3D cumulative isomerization probability N(E) for the transfer of a light particle between two atoms is computed by one time-independent and two time-dependent versions of the transition state wave packet (TSWP) method. The time-independent method is based on the direct expansion of the microcanonical projection operator on Chebyshev polynomials. In the time-dependent TSWP methods, the propagations are carried out by the split operator scheme and the multiconfiguration time-dependent Hartree (MCTDH) algorithm. This is the very first implementation of the TSWP method in the Heidelber MCTDH package [G. W. Worth, M. H. Beck, A. Jackle, and H.-D. Meyer, The MCDTH package, Version 8.2 (2000); H.-D Meyer, Version 8.3 (2002). See http://www.pci.uni-heidelberg.de/tc/usr/mctdh/]. The benchmark is the HCN-->CNH isomerization for zero total angular momentum. Particular insights are given into the tunneling region. In larger systems, the time-dependent version of TSWP making use of the MCTDH algorithm will permit to treat more and more modes quantum mechanically, for very accurate results. Therefore, it was important to calibrate the implementation. Besides, we also assess the efficiency of a reduced dimensionality approach by comparing the new exact 3D calculations of N(E) for the HCN-->CNH isomerization with results obtained via 1D or 2D active subspaces. This suggests that, it should be possible to take directly benefit of the present 3D approaches, adapted for triatomic Jacobi coordinates to compute N(E) for H-transfer in larger systems, via three active coordinates. The prerequisite is then the simplification of the reduced 3D kinetic energy operator with rigid constraint to take the form corresponding to a pseudo triatomic system in Jacobi coordinates with effective masses. This last step is checked in the methoxy radical and malonaldehyde. Finally, different ways to obtain reliable eigenvectors of the flux operator associated with a dividing surface are revisited.