Then I would use the "Compound Blur" effect to my footage, which is sitting on layer V3. In the "Effect Controls" of the Compound Blur, I would select "Video 2" for the Blur Layer option. On layer V2, the color matte that I had created earlier needs to be nested for the Tilt Shift Effect to show properly. If I didn't nest it, then my footage would be completely blurred (see the comparison below). So my question is, what does exactly nesting the color matte do, in relation to the footage in the layer above it?
Without seeing the tutorial, it's difficult to say exactly, but I think what is happening is that the colour matte nest that you've created, is being used to control the blur on your other layer, probably by being set to being used as an "alpha matte". If your colour matte layer wasn't nested, I think Premiere wouldn't be able to see the alpha changes on that layer, due to the order in which processes are rendered in its pipeline.
Effectively, by nesting the matte clip, the compound blur "sees" the effect and the matte as a single piece of video to process. Without it, it would only "see" a solid colour block.