β-delayed γ-neutron spectroscopy has been performed on the decay of A = 84 to 87 gallium isotopes at the RI-beam Factory at the RIKEN Nishina Center using a high-efficiency array of 3 He neutron counters (BRIKEN). β-2n-γ events were measured in the decays of all of the four isotopes for the first time, which is direct evidence for populating the excited states of two-neutron daughter nuclei. Detailed decay schemes with the γ branching ratios were obtained for these isotopes and the neutron emission probabilities (Pxn) were updated from the previous study. Hauser-Feshbach statistical model calculations were performed to understand the experimental branching ratios. We found that the P1n and P2n values are sensitive to the nuclear level densities of 1n daughter nuclei and showed that the statistical model reproduced the P2n/P1n ratio better when experimental levels + shell-model level densities fit by the Gilbert-Cameron formula were used as the level-density input. We also showed the neutron and γ branching ratios are sensitive to the ground-state spin of the parent nucleus. Our statistical model analysis suggested J ≤ 3 for the unknown ground-state spin of the odd-odd nucleus, 86 Ga, from the Iγ(4 + → 2 + )/Iγ(2 + → 0 + ) ratio of 84 Ga and the P2n/P1n ratio. These results show the necessity of detailed understanding of the decay scheme, including data from neutron spectroscopy, in addition to γ measurements of the multi-neutron emitters.