Things can be teken into two parts: (switching effect and charges in the channel)
1. At beginning, Vd=Vs=0, then Vg starts to decrease. Befoer Vg hit the Vth, channel is still there, which means the drain and source are connected by a on resistance (on resistance values changes). since Vg changes dramatically at this period, it make drain voltage changes as well. High freq signal pass through cap. This is one part of the current. The other part of the current is from the discharge of the Cgs.
2. Charges in the channel. In my opinion, they are still flow to decrease the drain-body depletion region. Since the drain voltage become negative, which almost make the drain-body diode forward biased. It needs charges to fill the depletion region. That's the place where the channel charges go.