The tappets are supposed to be self-adjusting. They fill with oil (I think you should fit new ones "pre-filled") and then as they are squeezed by the rocker arm during use, the end-cap is compressed and that forces oil out until the tappets are the right effective length to float on the rocker arm.
As there is wear, the spring is always trying to press the cap outwards, so the tappet will self-adjust. The void behind it is filled with oil, which gets sucked in, to maintain the new effective length.
Make sure the old tappets don't have a blocked oil channel and make sure that the end-cap is not jammed. I doubt it's a collapsed spring.
If you dismantle the tappet you may find a spring and also a ball bearing which can be tricky to re-assemble, so buy new tappets unless they're a horrific price.
Ralf S.