Okay... first thing is terminology.
The silver thing in your video is the fuel filter. The thing that makes the whirring noise and makes the fuel go round is the fuel pump. The injectors are not in the tank, there are two and they are in the throttle bodies.
The way the fuel system works is the pump moves fuel through the filter, out to the injectors and back to the tank. Pressure is set by a thing called a fuel pressure regulator that I think is near the throttle bodies on your bike (the principle design is the same for almost all of the fuel-injected Ducatis, even the old Pasos but the location and physical dimensions vary a little between years and models).
The pump can put out ~70 or so PSI, but the fuel pressure regulator bleeds off pressure to keep it at ~43.5 PSI.
The return line includes a pipe that dumps the fuel relatively far away from the fuel pump pickup in the steel tanks that I have seen (not counting the flanged bikes, but yours isn't one of those).
I would reach my hand in there and attempt to find the pinpoint spot where the fuel is coming out. If you don't mind a little loss of feel and added "safety" you can wear a nitrile glove to keep the gasoline off your skin. It's hard to tell what's going on without more info.
Did you transfer the pump/filter/hoses/etc. from the old tank to the new, or did you have a shop do it? I ask because you have the annoying "one-time" hose clamp on your fuel filter... It is possible one of the other hoses in the system is not adequately attached.
What happens when you try to start it?
BTW, introducing yourself to the other folks that are actually friendly might help
http://ducatimonsterforum.org/index.php?board=14.0