No, I am not talking about jello.
The thing is that the lens distortion (after stabilization) causes this wobble, that I am talking about:
At the top of the image (and left, right and bottom for that matter) there is more distortion as there is closer to the center of the image.
If you stabilize the footage, the footage is actually displaced (and zoomed) in by the software a bit in order to remove the "shake".
However, a change of direction of the lens, changes the amount of distortion. If the horizon is perfectly in the middle, it is horizontal, if you tilt down or up, the horizon becomes more "round", increasing distortion with increased tilt angle.
Now, if you stabilize your tilt (compensation for vertical displacement), you will see the horizon "wobbling", because at different positions in the original frame, it has a different "shape", roundness, distortion.
So, no matter how good your stabilization software is, it needs to be aware of the typical distortion of the lens used, or else there will be "wobble".
In other words, if your perfectly horizontal level lens keeps the horizon perfectly horizontal without distortion at all tilt levels, no wobble. (and the same for vertical of course). So, any lens with barrel or pincushion distortion will cause wobble. However, with extreme distortion as the PV lens it is really attraction attention. With some other lenses, or different POV of the PV lens it is not really annoying.
In my attempt, in my previous post, i first tried to remove the distortion, so the stabilized version would not have wobble. I succeed only partly, probably because I could not determine the correct lens distortion parameters. (I don't actually have the camera to try to get the correct parameters)
Now, if the Adobe lens thingy is 100% correct in adjusting for distortion, this would give (in theory) a wobble free stabilized footage. But I did not try this myself, because in my setup (old photoshop) it would take days to render a movie with decent quality with the Adobe lens correction applied.
I hope someone else tries and will show the results.