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 ωpump on the Floquet Dirac cone of graphene is disclosed from the transient absorption spectroscopy (TAS), which is due to the correlation between 2 ωpump-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.