This question already has an answer here:
The badges we earn are displayed over the achievements dialog (top of screen, leaderboards logo), but if we view them over another Stack Exchange site's page, we get shown THAT Stack Exchange site's logo of that badge.
For example, in the picture, I won a badge on Arqade, but when I open the dialog in Movies.SE, I see Movies.SE's (silver) badge, not Arqade's (silver) badge.
How it should look like:
It is nothing big or critical, just a small bug.