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.
EFR Twin Turbo LFX-GPI Tune-ZL1 fuel pump-10:1 CR forged pistons-3.45 gear-Meth Injection-BMR Trailing Arms, Bushings & Sway Bars-CircleD 4000 Stall-GPI Fuel Enrichment System
647 RWHP & 726 RWTQ @18.5 psi on 93 Octane (locked converter)
1/8 mile -- 7.158 @ 102.10 (20psi); old build