The most likely cause is that the camera was being moved slightly before the exposure had fully finished. Since the streaks were always straight and always to the right—the same direction as your pan—that points to motion from starting the next rotation too soon, not tripod instability.

With a DSLR, the shutter/mirror sequence can be easy to misread by sound alone. If you begin turning the camera after the initial click but before the rear curtain has fully closed, bright point lights can smear into short streaks in the direction of movement.

So the fix is simple: wait until the entire shutter cycle is complete before touching the camera to pan to the next frame. In practice, that means listening for the full mirror/shutter sequence to finish, not just the first click. A slightly longer pause between frames should eliminate the one-sided light trails.