Ultrafast dynamics in the Floquet states of Dirac semiconductors are theoretically explored, which accentuates nonequilibrium dynamical nature of the Floquet state beyond the usually considered quasi static band nature and then gives a missing connection between the two. Phase oscillation of the Fano resonance at the frequency of 2 omega(pump) on the Floquet Dirac cone of graphene is disclosed from the transient absorption spectroscopy (TAS), which is due to the correlation between 2 omega(pump)-absorption paths. This establishes a driving of the petahertz (PHz) quantum oscillation from Dirac materials. On another Floquet Dirac cone of the graphene/h-BN (Gr/h-BN) heterostructure under the circularly polarized pulse pumping, we find a regime that exists between topologically trivial and optically induced nontrivial phases from the time-resolved dichroic photoemission spectroscopy (TRdPES), which we call the fluctuating topological order. The topological order fluctuation is a novel mixed phase, i.e., a dynamical mixture of trivial and nontrivial phases, as a precursor to the transient nontrivial phase. (C) 2021 Published by Elsevier Ltd.