For the 35 rumble seat cars there is nothing to catch the water, it does run down behind the seat. Just to the rear of the bottom seat cushion is a water dam that prevents the water from moving forward and under the seat cushion, it is screwed to the floor at the floor seam. The dam also has two tabs that attach the lower seat cushion spring set so the rear of the seat does not come up.
There is an early dam design and a mid year design that was carried over to 36. Nearly all of the original 35 rumble seat cars have the floor to the rear of the rumble bottom cushion rusted out because Ford in 35 did not have a drain for the water.