As said INA are oe kit makers of tappets.
Castrol oil is crap, you want SILKOLENE PRO S 10W/50, recent tests showed that the worst performing oil for retaining it's synthetic qualities was CASTROL head and shoulders worse than any other, then SHELL HELIX, Mobil 1 did better, but only just.
I have used tappet lube from WYNNS in the past to excellent effect, as well as engine flush, and the head that came off mine recently had not one single spec of carbon anywhere, nothing at all, despite 16 worn valve guides and 8 knackered valves(exhausts).
It is not unusuall for the tappets to tap for a few seconds when cold, so long as it goes when hot that is the main thing, but as said they still do not last forever.
Just be sure you get ones intended for the cossie and not VW ones which are dimensionally identical, but operate on a different pressure, and never seem to be as quiet.
tabetha