The lifetime of the ${9}^{\ensuremath{-}}$ state in the rotational band based on the 4.0 s, ${K}^{\ensuremath{\pi}}={8}^{\ensuremath{-}}$, isomeric state ($^{178}\mathrm{Hf}^{{m}_{1}}$) from the decay of the 31-yr isomer ($^{178}\mathrm{Hf}^{{m}_{2}}$) was determined to be 99(2) ps by means of the fast-timing technique using two ${\mathrm{LaBr}}_{3}$(Ce) scintillators. The $\ensuremath{\delta}(E2/M1)$ mixing ratios of the $\mathrm{\ensuremath{\Delta}}I=1\phantom{\rule{4pt}{0ex}}\ensuremath{\gamma}$ rays depopulating levels in this band were deduced from $\ensuremath{\gamma}\text{\ensuremath{-}}\ensuremath{\gamma}$ angular correlations by using a $^{178}\mathrm{Hf}^{{m}_{2}}$ radioactive source located at the center of the Gammasphere HPGe detector array. The new results, together with previous spectroscopic information, provide a different way to extract the intrinsic quadrupole moment of ${Q}_{0}=6.45(14)\phantom{\rule{4pt}{0ex}}e\text{b}$ for the $^{178}\mathrm{Hf}^{{m}_{1}}$ band. A possible explanation for the reduction of the $^{178}\mathrm{Hf}^{{m}_{1}}$ nuclear charge radius is presented.