Originally Posted by
Qualia
AU Draenor is in our / the Legion's present, but it was the past in that alternate universe. When we traveled over, we actually crossed both space (from our MU to the AU) and time (from present to past) and so was the Legion. The later part is "time travel", unless our definitions of time travelling differ somehow. We just don't know if the Legion can do it freely in other alternate universe, or this is just a chance unintentionally created by Kairoz that they grabbed. As of time travelling in our universe, they can probably do that, seeing that even mortal mages can. I'd expect the Bronze Dragonflight to prevent any unnatural change to history if the Legion messed with our past, though, just like they (well, Nozdormu) did when the Old Gods tried.
As of your theory that MU is the only one with a world soul, and that if it's the case, AU Azeroths would be very different from ours - there is an issue with it as we've seen alternate version of some important characters. Kairoz summoned an alternate self of Kalec that knew Aveena, so in that AU there was a Sunwell (and thus, likely had the WoE) and influence of the Titan (the Aspects / dragons wouldn't have became dragons otherwise). Vandel saw, in his visions of the multiverse, that there were "countless Azeroths, countless Vandels, and countless Khariels, and to every one of them came death" so elves (and thus, WoE) should have been around in those AUs as well. While it might not be true that every Azeroths have a world soul, there are likely more than one of them with it.