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One of the promising fields of nanophotonics is studying metasurfaces optical response on external stimulus such as a femtosecond laser radiation. Ultrashort pulse heats electron gas of metals and modifies dielectric permittivity. The induced changes can be observed by probing reflectance or transmittance. Metasurfaces are sensitive to dielectric permittivity changes near a resonance, therefore they can be used to significantly enhance optical response. Moreover, electromagnetic field localization within a medium in metasurfaces provides the stronger impact of an incident laser pulse on a structure. Evolution of a plasmonic metasurface optical response is described by the hot electron dynamics of the corresponding bulk noble metal. Additional ultrafast processes may appear due to nanostructuring or excitation of electromagnetic modes like vibrational resonances of nanospheres or plasmon-induced electron transfer from nanoparticles to semiconductor. In the multicomponent systems, like hybrid metal-dielectric metasurfaces, it is possible to excite both plasmon and polariton modes. Response of these modes on the same medium perturbation can differ significantly. Therefore, the presence of several processes in hybrid metasurface leads to diverse dynamics of the optical response in the vicinity of resonances of different types. In this work, diverse ultrafast dynamics of the optical response are experimentally observed in a hybrid metal-dielectric Au-Bi:YIG metasurface by probing at the frequencies of polariton and plasmon modes. Plasmon modes demonstrate typical for bulk gold transmittance dynamics, meanwhile anomalous dependences on time delay and pump fluence were detected in the narrow spectral window corresponding to the excitation of polariton mode by a probe beam. Transmittance evolution in this window is slower, and tends to be more pronounced with increase of pump fluence. Transmittance dependence on fluence shows sublinear behavior, while it is linear for plasmon modes, as it to be expected for bulk gold.