The neutron-deficient Hg isotopes provide one of the most prominent examples of nuclear shape coexistence. While the even-even nuclei have been extensively investigated, much less is known about how an unpaired neutron influences the evolution of collectivity in the odd-mass isotopes. To determine lifetimes of low-spin states in ${}^{189}$Hg and investigate the evolution of collectivity in the rotational band built on the $13/2^{+}$ isomer through comparison with neighboring shape-coexisting Hg isotopes. Excited states in ${}^{189}$Hg were populated in the ${}^{160}$Gd(${}^{34}$S,5n)${}^{189}$Hg fusion-evaporation reaction at a beam energy of 185~MeV. The reaction channel of interest was selected by requiring coincidence with at least one neutron detected in the Neutron Wall array, while prompt $\gamma$ rays were measured with the GALILEO spectrometer. Lifetimes of low-lying states above the $13/2^{+}$ isomer were measured with the recoil-distance Doppler-shift method using the GALILEO plunger device. The experimental results were compared with Total Routhian Surface calculations. Lifetimes of the $17/2^{+}$, $21/2^{+}$, and $25/2^{+}$ states were measured for the first time and the corresponding B(E2) strengths were extracted. The excitation energies and transition strengths closely follow the systematics observed in neighboring odd- and even-mass Hg isotopes, supporting the interpretation of the rotational sequence as the coupling of an $i_{13/2}$ neutron to the weakly oblate structures of the neighboring even-even cores. The extracted $B_{4/2}$-type ratio is significantly below unity, extending the occurrence of anomalous transition-strength ratios to this odd-mass nucleus. Total Routhian Surface calculations reproduce the weakly oblate equilibrium deformation but not the observed evolution of the transition strengths. The present results indicate that the $i_{13/2}$-based rotational band largely inherits the structural complexity of the neighboring shape-coexisting even-even Hg nuclei. They further demonstrate that electromagnetic transition strengths provide stringent constraints on the evolution of the underlying wave functions beyond those accessible from excitation energies or static mean-field descriptions alone.