OK, just been looking at an old one...
the outer housing is solid at the bottom and has a bore inside, it'e waisted in the middle and fits the hole it slides in top and bottom. In the middle bit is a small hole.
Inside, from bottom to top, are a spring and 2 separate hollow pistons, the upper piston has 3 small indents which mean that when it sits on the lower one, there are 3 small holes. Alongside the tappet hole is a pressure oil gallery. The oil clearly gets in through the hole in the side of the tappet, and from there works its way into the inside of the piston, through the 3 little indents.
I assume that surplus oil finds its way out of the tappet past the upper half of the piston, which has no obvious seal.
now the bit that's puzzling me... I can see that when the engine's running and the valve's open, the tappet "pumps up". what I want to know is, how does it let the valve shut?
Is it just that it leaks at a pre-determined speed, such that the normal oil pressure is not too much to overcome the valve springs pushing back down the pushrod?
and now another point: I've a set of non-rover replacement ones, which have been running for about 20K miles. These, compared with the one I've just pulled apart, have a smaller oil feed hole in the side, but they also don't appear to compress against the internal spring the same as the rover ones. I assume they have some oil in 'em, since they've been used, but they can't be under pressure.