The metal tube on the fuel pump housing assembly is not sealed properly against your fuel pump. Fuel pump o-ring is the culprit.
What Reza is referring to is an o-ring which seals the outlet tube of the pump to (what eventually becomes) the fuel feed line that goes to your rail. If this seal is not sealing properly (for whatever reason) it should be fixed.
The thing is, that when the engine is running and your pump is putting out full pressure, if a little bit leaks out, because the pump generally delivers much more fuel than is actually used, if a bit leaked out (and it would be an internal leak, back into the tank) you'd never notice or care.
When your car sits for a long time, the fuel in the rail and lines can "leak" (again, an internal leak, so you can't see it) past the o-ring seal and back into the tank. So the next moring when you start up, the lines and rail must once again be re-filled (the "priming" you speak of).
Also, when running with mods that require more than stock amounts of fuel, the little bit that leaked past the o-ring that was not a concern because it was "extra", can suddenly become a concern when it is no longer extra, but actually required.
The point is, it's never a GOOD thing to have a leak at that seal. Even if fixing that seal doesn't cure your problem (you could have more than one culprit causing your condition), you should still definitely fix that seal.