By "frame", I mean in the conventional photography/cinematographic sense (field of view of a camera) or the traditional physics sense (as in a reference frame).
In your example above, there is an emitter following an object moving along a path. It makes it look like smoke is coming out of the object, and there's a plume. That's quite simple.
Assume that the ball is stationary and you place place a particle emitter on it to general smoke. If you move the ball left, the emitter also move left, and the particles at the emitter's original location move straightup and new particles are emitted in the up direction along the path. That makes sense if the ball was moving, but if the ball appears to move left because the camera is panning right, the emitted particles shouldn't be spread between the emitter's start and stop locations, the particles should move with the emitter.
The really tricky part is that the camera is panning (in the sense of the shot for the scene) AND the object in the shot that the emitter is tracking, are BOTH moving. So, the velocity of the particles should be their velocity as they come off the emitter PLUS the velocity of the movement of the scene.
If you had a shaky shot you could easily stabilize the scene to make sure it doesn't move, then setup your emitter path in that stationary scene. However, if you want to keep the movement of the scene from the original shot, you need the emitter to move relative to the object and correct the particle motion for the movement of the scene. If you don't, the particles follow a regular trajectory that's out of sync with the movement of the scene.
Mathematically, it's very simple, the particles have a velocity relative to the emitter. Within the scene, their realized velocities should be the velocity relative to the emitter plus the velocity of the change in the scene. This is what Motion Tracking gives you for objects and emitters, but I can't figure out how to make particles move to compensate for the motion of the scene. They don't "track" anything.
The obvious way would be to create a Motion Tracker that moves with the scene. Then create an emitter that follows and object in the scene, and then make the emitted particles trajectories match the movement of the scene. I can't figure out how to do that.