So I finished the civil war quests with the Imperial Legion, killed Ulfric and all that.
So now that everything is done, some of the Jarls (the Jarl from Dawnstar and the Jarl from Riften) and their stewards just sit in the Palace of Kings, doing nothing.
And when I go to Riften, the new Jarl is Jarl Maven Black-Briar, and the steward is Hemming Black-Briar. Is this supposed to happen if you complete the Imperial questline and kill Ulfric?
Or is this just a bug? Has this happened to anyone else?
Also, this is on the PS3.

Yes, it's supposed to happen.

What on earth made you think it was a bug? Didn't Maven's "This throne suits me, don't you think?" line make it obvious it was meant to happen?

Who gets replaced if you complete the Stormcloak side of the Civil War, by the way?

Whiterun gets a Greymane, Markarth gets a Silver-Blood, and... I forget.