Moving documents between document set does not propagate shared columns values

Hi, 

Did anyone tried to copy/move documents between documents sets and found out that shared columns values does not get updated? With my tests I found that copying/moving documents in documents set does not propagate values if the source document and document set destination are in the same library. However, if the source document is in a different library than the document set destination, it will propagate. 

This look to me as an important issue. Because I did not found anyone talking about this issue, I'm wondering if my tests results are accurate.

Thanks!