I'd suggest you export two instances of a scene. One - alpha of the moving Particular objects and one of the actual footage. Then use the alpha vid as a TrackMatte for the actual one.
You can choose to export Alpha in the render queue, under the chosen format. You have two options: RGB and Alpha.
The Alpha vid (or the TrackMatte) will control what parts of your actual footage are visible.
I hope it works out well. If you have any questions or anything regarding that feel free to ask. I'll try to help out, but i'm no pro.
Another way you can do it is just export with a black background, but i'm not sure if it will work as wanted.
Safe bruv, hit me back with the results, we'll think of something else if it doesn't work.
And hit me up if you need more detailed instructions, I'm not sure if i have expressed the steps in a coherent manner
