A recent report shows that the cyanine-based molecular rotor, PicoGreen, has very strong affinity toward amyloid fibrils and shows large increase in its emission yield upon binding with insulin amyloid fibrils. To gain deeper knowledge about the excited-state molecular processes that are responsible for its amyloid sensing behavior, detailed ultrafast dynamics of PicoGreen in molecular solvents with varying polarity and viscosity have been investigated. Our detailed studies on femtosecond time-resolved emission of PicoGreen show that both polarity and viscosity of the medium a play vital role in the deactivation of its photoexcited state. Detailed analysis of the time-resolved data suggests the formation of the intramolecular charge transfer (ICT) state, which is independent of solvent viscosity, takes place in ultrafast time scales (<2 ps), followed by the formation of a twisted ICT (TICT) state at a longer time scale in polar solvents. The formation of TICT from the ICT state due to the large amplitude torsional motion in its excited state has been supported by viscosity-dependent excited-state dynamics. Finally, the dynamical studies in fibrillar medium demonstrate the retardation in the excited-state torsional motion, which is primarily responsible for its observed large fluorescence enhancement in insulin amyloid fibrils.