I managed to run plotSipDistribution. In case someone read this, both conda and a local install of astrometry don't include mentioned util, so you need to pull it from Dustin's GitHub.
I exaggerated correction 10x on all of my images. With the "no_tweak" option, as expected, there is no correction(picture output_free_notweak.png). And, as I mentioned in my previous post, arbitrary RA&Dec coordinate is located in the same pixels, regardless of which index file is used to solve starfield.
With tweak order 2, SIP correction is different and depends on chosen index file(pictures output_free_tw2.png, output_fixed_tw2.png).
The same thing is with tw=4, only increased effect.
Dustin, if it is not too much to ask, what do the red lines represent (distortion correction)?
Because, in the index plot, after applying SIP corrections, green circles(where stars should be if there is no distortion) are shifted towards the end of the image, because distortion is causing the stars to appear further from the center of the image.
Now, looking at the SIP plot, red lines are moved toward the center.
I attached both index plots(with tw=2 and no tweak) and also SIP plots(with tw=2 and no tweak).
Note: SIP plot contains whole image, but index plot is only left part, where starfield is.