Omega is a throwback to FFV. It makes sense that the creature we'll have as a companion guiding us through this raid is Boko, Bartz very companion. This raid story revolves around Omega creating random stuff and sending us through multiple dimensions.
By the way, Alexander's plot revolved around a freaking cat and silly goblins.

So, yeah, Alpha's appearence doesn't fit in FFXIV. But that's the point. Omega talks to us via hoping TV monitors, random geometrical shapes fly through the area... Everything about this dimension doesn't make sense in FFXIV's world.
If you don't understand that, then you miss half the point of Omega's story.