Normally I'd say this isn't normal. However, considering you stated the suspension is lowered in your car, this may actually be something which is caused from it being lowered. Here's why I say this ...
When you lower a vehicle, you are allowing the suspension to get closer to the vehicle. This can be done by compacting the rear spring (putting in a spring which may have a higher spring rate, yet with less overall height and travel). Just because the rear spring is shorter, doesn't mean the travel of the rear suspension is any different. If, when the suspension is fully hung (not bearing any weight), such as what you show in the video, your springs may be completely off of the perches depending on how the the lower was done. If these are coil-overs, you probably wouldn't see this. If, however, these are lower springs which sit in the original perches, then the suspension might be all the way down and there may be a slight gap between the spring and the perch ... which would allow for the movement you show.
To verify this, securely put the vehicle up on jack stands, then crawl under the car while someone else moves the suspension so you can see what is actually happening. Look to where the spring is at the top. See if there is movement there between the spring and the body of the car (top spring perch).
If this doesn't prove to be what's happening, you may be able to actually see what's going on with it. You'd be looking for where ever the movement occurs. If there is movement where bushings are located, then there's an issue there. Just follow all avenues of movement and you should sooner or later find the culprit.
