I did some more testing and I think i found the problem with the vignetting (or at least some of it).
Sony’s explanation of the lens compensation feature includes:
Even though lens compensation will be applied to the JPEG file when shooting in RAW+JPEG, the RAW file remains uncompensated. If you wish having the corrections also applied to the RAW file, use the Sony Image Data Converter. Converted files can then be saved as lossless TIFF or as easy to handle JPEG file. 3rd party RAW converters might not be able to apply the corrections to the RAW file.
And indeed turning the shading compensation off and on had effect on the JPEGs. But it also affected the RAWs, despite what Sony says. So the vignette correction might be applied twice.
Doing a quick check it seems Adobe’s LCP + build in shading compensation works better than just the LCP. This might indicate that Adobe sampled compensated RAWs. In comparison lens fun (at least for the 50mm lens) correction gets better results if the shading compensation is off (which might be expected). However, it still over-compensates in my opinion.
This is a bummer, because if you shoot RAW+JPG you need to enable all the compensation as otherwise they won’t be applied to the JPGs.