Time displacement effect on linked object

Time displacement remaps the time of e.g. an animated pre-composition pixel by pixel, but otherwise the methodology is pretty much the same. A simple gradient will give what is known as a slitscan effect, i.e. offsetting each row of pixels by the amount of time delay/ a frame. In your case quite likely the problem simply is that you may need to use a more elaborate mask and also pre-compose whatever you are animting there. It's really not quite clear what you are even trying to achieve.

Mylenium

Displacement maps move pixels based on the luminance or brightness of a color. If you look at the Brightness value in the Color Picker or under the cursor in the Info Panel, if you set the display to percent, anything above 50% moves the pixels in one direction. Anything below moves them the other.

the effect doesn't care, but without any info on what tutorials you are following, screenshots of your timeline and displacment map and all that good stuff nobody can tell you much. Just showing a cropped snippet oif the result is pretty much useless. From what can be discerned in your image there's simply a size mismatch between the source layer and the displacment map, but why and how is impossible to determine without further details.

Mylenium