Local magnetostructural changes and dynamical spin fluctuations in doubly diluted spinel Ti x Mn1‒x (Fe y Co1‒y )2O4 has been reported by means of neutron diffraction and magnetization studies. Two distinct sets of compositions (i) x(Ti) = 0.20 and y(Fe) = 0.18; (ii) x(Ti) = 0.40 and y(Fe) = 0.435 have been considered for this study. The first compound of equivalent stoichiometry Ti0.20Mn0.80Fe0.36Co1.64O4 exhibits enhanced tetragonal distortion across the ferrimagnetic transition temperature T C = 258 K in comparison to the end compound MnCo2O4 (T C ∼ 180 K) with a characteristic ratio c t/√2a t of 0.99795(8) demonstrating robust lattice-spin-orbital coupling. However, in the second case Ti0.40Mn0.60Fe0.87Co1.13O4 with higher B-site compositions, the presence of Jahn–Teller ions with distinct behavior appears to counterbalance the strong tetragonal distortion thereby ceasing the lattice-spin-orbital coupling. Both the investigated systems show the coexistence of noncollinear antiferromagnetic and ferrimagnetic components in cubic and tetragonal settings. On the other hand, the dynamical ac-susceptibility, χ ac(T) reveals a cluster spin-glass state with Gabay–Toulouse (GT) like mixed phases behaviour below T C. Such dispersive behaviour appears to be sensitive to the level of octahedral substitution. Further, the field dependence of χ ac(T) follows the weak anisotropic GT-line behaviour with crossover exponent Φ lies in the range 1.38–1.52 on the H–T plane which is in contrast to the B-site Ti substituted MnCo2O4 spinel that appears to follow irreversible non-mean-field AT-line behaviour (Φ ∼ 3 + δ). Finally, the Arrott plots analysis indicates the presence of a pseudo first-order like transition (T < 20 K) which is in consonance with and zero crossover of the magnetic entropy change within the frozen spin-glass regime.