Rare-earth based garnet system, Ho3Fe5O12 shows magnetization compensation phenomenon at Tcomp = 138 K and a magnetic transition at 50 K. In the present work, we reveal the physics of these low temperature magnetic transitions by carrying out detailed dc magnetization, ac susceptibility, neutron depolarization, and neutron diffraction studies. Interestingly, our dc magnetization study under low (≲ 50 Oe) magnetic fields has shown a previously unknown sign reversal of magnetization (below the Tcomp) that persists down to 5 K, the lowest measured temperature. Magnetic measurements under moderate fields between 50 Oe and 1 kOe reveal two compensation temperatures (in the range of 105 – 150 K depending upon the applied field value) leading to double magnetization reversals. Interestingly, for magnetic fields ≥ 1 kOe, these two compensation temperatures merge to a single Tcomp (=138 K). A modified Stoner-Wohlfarth model has been used to explain the asymmetrical nature of double peak around the Tcomp in the temperature dependent coercivity data. The ac susceptibility study supports the existence of both the transitions with an evidence of deep minimum at the Tcomp (138 K) and a broad peak at 50 K. Mesoscopic neutron depolarization study has revealed a zero domain-magnetization state at the Tcomp. Temperature dependent neutron diffraction study has revealed that Ho carries an induced moment above the Tcomp due to polarizing effect under the internal magnetic field of the two magnetically ordered Fe sublattices at 567 K, whereas a single umbrella type ordering of Ho sublattice moments appears below the Tcomp, resulting in the distortion of magnetic unit cell from cubic to rhombohedral symmetry. However, below 50 K, Ho3+ sites are divided into two inequivalent magnetic sublattices, having different moments and canting angles, and it leads to double umbrella type magnetic structure. Neutron diffraction study has revealed an asymmetric variation of the tetrahedral, octahedral, and dodecahedral sublattice moments resulting in a magnetization reversal at ~ 138 K which is very well supported by the mean field theory calculations. In the present study, we have resolved the ambiguity of magnetic ordering of the rare-earth (Ho3+) sublattice and its role in multiple magnetic transitions. The utility of such compensated ferrimagnetic materials in spin polarizers/analyzers and fast switching memory devices has been emphasized.