When I used my EU2000i while dry camping the first time, I did not see any fuel movement for a while. Went in to the trailer for about 30 minutes and came out to check and the clear fuel line was full. I think it must take a while for the built in tank to empty a bit before there is enough suction to draw from the auxiliary tank.
I don't know anything about the fuel pump so can't help you there, however my feeling is that the fuel is not "pumped" from the auxiliary tank but instead is "drawn" or "sucked" out of it because of a vacuum formed in the regular tank. Make very sure there is no air leak in the cover of the generator tank.
Barney