You have two fuel pumps. One is a low-pressure "lift" pump that's in the tank. The other is the high-pressure pump for the direct injection that's located at the back of the passanger-side cam (behind some baffling). If simply turning on the key for a few seconds before you start it solves the problem, then it is not the high-pressure pump -- it is mechanical. I would have them make sure they got the check valvle replaced (I believe there is one) before removing the tank to replace the lift pump.
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