I have a profile picture set on site A, and a different profile picture on site B. Site A is my default parent site, so it's the one that should show in all chat windows. However the image seemingly randomly changes to that of site B when I click "automatically move comments to chat" on a particular answer's comment thread. The only thing I can tell about that comment thread is that someone else already tried to move comments to chat, but deleted that comment. When I click it, a new comment doesn't appear with a link to the chat, but my profile picture changes for all chat sites I am on, and all the chat windows reload. I can consistently reproduce this by trying to move comments to chat on this answer.
The interesting thing is that my parent site still shows as site A when I look at my user settings, but what is displayed is that of site B. I have to switch my default parent site away and back to fix this.
Update: It just happened (on the Cryptography site) when I tried to automatically move comments to chat, but at this time, the new comment with the chat link did appear, so my above hypothesis regarding there already being a deleted chat comment is likely incorrect.