hydraulic valve lash adjusters need oil to work. kung di nag-circulate ang oil madre-drain nga yung oil dun sa loob ng adjusters and magkakaron ng tappet sounds (takatak or tik-tik, depends on how severe). engine oil acts as the hydraulic fluid inside the lash adjusters (it is like a piston inside a cylinder with a spring inside) and it is this amount of oil inside that "adjusts" the valve clearance. pag walang oil ang mangyari lang dun e lalaki yung valve clearance kasi nga depleted yung oil sa loob ng hydraulic lash adjusters. now as you said after the oil began circulating again the tappet sounds disappeared. that is normal since again oil went inside the lash adjusters and they started working again. however as you said the casa people said "tope", there is a possibility that since the adjusters ran without oil that they will need replacement, baka may leak na or pwede din mag-seize and hindi na maga-adjust. sabi din nila baka sira ang valves? mangyayari yan pag sobrang laki ng clearance nung hindi nag-adjust yung haydraulic lash adjusters at na-hammer na yung valve stem. the damage will be on the valve stem, not on the valves or pistons (na typically nangyayari pag naputulan ka ng timing belt). anyway if this is the case (damaged valve stems) wala ka kawala sa top overhaul (pwede palit lang ng valves and lash adjusters, and of course head gasket. di naman nag-overheat ang engine mo so di need ang machining.

i am more concerned with the oil not circulating. was it just not enough wherein the lash adjusters ran out of oil, or was it worse and the bearings did not get enough oil? if the case is the later than you are in for a major overhaul, maybe even major parts replacement. i suggest have the casa check your engine thoroughly and if worse comes to worst then sell you car na lang. sorry ganun talaga e. sana naman hindi.