Comment 12 for bug 1059475

I had the same issue but this upgrade fixed it after log out -> in.

If webapp is added as a launcher in Unity, first the Chromium icon appears besides it and then disappears, leaving "control"
to the appropriate launcher.
If launched from dash or messaging menu, the Chromium icon appears and then "transforms" into
the appropriate icon.

Possibly unrelated, I must add I had previously upgraded also chromium unity extensions from raring-proposed, mentioning just in case.

$ apt-cache policy bamfdaemon
bamfdaemon:
  Installed: 0.4.0daily13.06.19~13.04-0ubuntu1
  Candidate: 0.4.0daily13.06.19~13.04-0ubuntu1
  Version table:
 *** 0.4.0daily13.06.19~13.04-0ubuntu1 0
        500 http://es.archive.ubuntu.com/ubuntu/ raring-proposed/main amd64 Packages
        100 /var/lib/dpkg/status
     0.4.0daily13.04.03-0ubuntu1 0
        500 http://es.archive.ubuntu.com/ubuntu/ raring/main amd64 Packages