There are several ways. You can animate the blend with original property in many effects. It's usually at the bottom of the Effects Controls. You can create a mask the covers the entire clip by double clicking the rectangle mask tool and then use the Compositing options to add the mask to the effect in the timeline in CC2014 or later. You can add an adjustment layer above the layer you want to add your red tint to and then pre-compose the pair then add the tint effect in the Pre-comp and trim the in and out points of the adjustment layer or animate it's opacity. You could simply put a red solid with a color blend mode on top of your video and edit the in and out points and opacity.
These are all AE basic skills you should learn. There is no magic here, it's just basic procedure.
here's what using a mask to control an effect in CC 2015 would look like: