Take the tappets out, soak them overnight in white spirit, upside down. Then remove the inside plunger with pliars or by banging on a wooden surface. Pull the plungers apart and clean inside, test the one-way valve operates correctly by blowing/sucking and completely clean in white spirit, then after all components are cleaned, clean again with brake cleaner, then dry on the radiator. Then reassembly is the reverse of the process. Refresh the surface that contacts the camshaft by scribing a figure of 8 on a lubricated whetstone until the surface uniformly dulls-up. Once you've done that and all the one-way valves are proven working, and all the tiny springs are working and not split, you know you've got 16 working followers.
These followers do not need 'priming' because when engine oil under pressure attacks the ball bearing one-way-valve, the air will come out the same hole the oil goes in and the valves will bleed themselves. Can take a couple of minutes, make sure you change your oil and filter at the same time because it'd be a shame to crap-up your shiny new tappets!
...of course it's probably the head gasket on the wrong way round, especially if you think it won't go on wrong! I did it once, so nobody is immune
Good luck!