I finished the "claw" Barrow Temple quest yesterday, and went through the whole thing, killing the Draugir at the end, and getting the word from the wall.

When I reached whiterun, I was given a quest by the mage to get a dragontablet. Well, it turns out it was in the same dungeon! So I walked through the dungeon (everything was dead) and got to the end. The last Draugir had it in his inventory, and I guarantee it wasn't there before.

Is this bugged, or was it assumed I wouldn't be able to finish the dungeon until I had gotten to Whiterun?

The dragon tablet spawns before you take the quest. You just missed it.

Weird, I am sure I looted the Draugir, just didn't see it.

yeah I allready had it when I got to whiterun
just looked important I guess