I dont think in Toyota the pump pressurized the fuel line when you switch on ignition. In Honda it happens but not in toyota as far as i know..
Sputters can be caused by low fuel line pressure or leaking injectors as well. I had similar issues in one of my car it will sputters for few seconds on morning startup than it will be fine. The leaking injectors will leak some petrol in the cylinders and also lose the fuel line pressure causing this.
If nothing works try getting the injectors cleaning by a ultra sonic machine.