Sounds odd... my 7PSI Carter pusher pump is also wired directly into the same circuit as my factory lift pump, and I have had it for about 15 months now, and never once had any issues with starting. As soon as I move the key to the wait-to-start position, both pumps run for a split second, and I see pressure register on my fuel pressure gauge, but then they both stop and I have 0 PSI, and I don't hear the pusher running. And believe me, it is loud. When I am standing next to the truck while fueling it up, I almost always leave the engine idling, and I can easily hear the pusher buzzing merrily away, even over the engine noise!
Tom