How does inlet spillage drag produce a lip suction effect?
Yes, your last sentence gets it about right. Just one detail: Air does not move "forward" to flow out again once it has entered the intake - which air goes where is all settled ahead of the intake. Never forget, though, that this effect is small and spillage leaves a net drag component.

When compared to a sharp-lipped intake as used on supersonic planes, subsonic intakes are more forgiving for a mismatch between capture area (area of the stream tube which goes into the engine) and the actual intake lip area. Below I tried to fake the flow around an intake lip using Inkscape and added blue and red shading to indicate pressure. The core flow gets compressed ahead of the intake (blue shade, diverging streamlines) while the outer flow is pushed to the outside of the intake lip by the increasing pressure and now has to follow the contour of the intake. Like with air flowing around the upper side of an airfoil, the air is accelerated (converging flow lines) and a suction peak forms on the intake lip (red shading). This suction peak sits on the forward-facing part of the intake lip and provides some suction.

The sharp intake lip of a surpersonic intake would produce separated flow under the same conditions with a considerable increase in drag.