It's all a matter of numbers and availability. There are many more Vascular Surgeons than Interventional Radiologists.
The procedure itself is fully guided by the "traditional" Radiological Angiographic techniques, which the IR's do day in/day out every day of their lives.
In my institution, the procedure is done in an specially designed OR (C-Arm included) and is directed by the IR. A Vascular Surgeon opens and closes the vascular access (since, contrary to the usual transfemoral puncture, the access has to be pretty damn big for the device). And is present during the rest of the procedure. The remainder of the procedure (as it is done from inside the Aorta) is run by the IR (Aortic Runs, deployment of the device, etc.)
So, essentially, it is a team effort between the VS and IR. But the show is run by the IR. The VS is only in charge of the access.
Of course, whenever there is a successful procedure which pays well, you will see every specialty trying to get access to it somehow. Sadly, far from being a collegiate group of professionals, real world medicine is all about turf wars. The above procedure is only a teeny tiny example.