In principle, this should have nothing to do with Developer Tools per se.
Do you see the favicon on the tab? I just checked and the favicon is there (not on the location bar).
In these cases the best thing to do is to file a bug in Bugzilla. If it’s duplicated, it will be marked as such. If it’s not, someone will get to it!
You can file it here: https://bugzilla.mozilla.org/enter_bug.cgi?product=Firefox&component=Tabbed%20Browser