If the tensioner has partly lost adjustment then that would weaken the spring pressure on the belt.. (you can check by confirming whether the tensioner pointer is still pointing at the reference hole) but you only need the correct spring tension to make sure the belt isn't able to jump off the pulley (which would very likely wreck your valves, not just cause them to "tap" the pistons) so I don't think it's the tensioner in this case.
The car has hydraulic tappets. A hydraulic tappet is a cup with a plate that's fitted into it (and which is able to move in and out), held under a small tension via a spring and a ball bearing. The plate has a pimple on it that sits on the cam lobe. The plate is held in the cup by nothing more than a "pinch" on the open end of the cup.
The tappet fits into an apperture in the head, above the valve, with the plate/pimple resting on the valve and the top/flat face facing the camshaft lobes. The tappet can rotate in the apperture and this allows wear/force to even out.
When the tappet apperture fills with oil, oil enters and fills the tappet cup via a small hole in the side. When the cam lobe acts on the tappet face, it presses the cup downwards. The plate is consequently pressed onto the valve.
This squeezes the spring inside the tappet and the oil in the cup is forced out of the hole... but since the hole is tiny, the oil flow outwards creates a resistance to the force of the cam lobe on the tappet and it doesn't all get squeezed out.
As the tappet face and the plate pimple wear (the tappet becomes microscopically shorter), the spring moves the plate outwards so that the tappet "length" stays constant.
So it's acting like a mini "valve".. keeping a constant length despite wear, or the operating pressure from the cam lobe.
There's a few things that can go wrong. If the oil hole is partially blocked, the oil can't get back into the tappet after it's been squeezed out slightly (under pressure from the cam lobe). Note there is nothing "forcing" the oil back into the tappet.
If the plate becomes jammed inside the cup, then the tappet can't adjust itself to compensate for wear to the pimple or the face. Similarly, if the tappet plate reaches the "pinch" at the end of the cup (e.g. maximum wear) then it can't travel out any more, so the tappet becomes technically too short.
In extreme cases the cup can jam in the cylinder head (so it can no longer rotate) and so the wear is concentrated in one spot.. it's unlikely the plate will also not jam inside the cup and so you again get the symptom of a short tappet.
A short tappet acts like a badly adjusted tappet in the old days of cam-followers (or more analagously) valve shims.. and as my old mechanic used to say "Knock Knock; camshaft, Tap Tap; tappet".
Ralf S.