so for some actual help:
no there is no adjustment on the rockers for the 1.5L that i can see. i believe they are hydraulic lifters which cannot be adjust as they don't need it. the valve lash is adjusted by the oil pressure.
**if anyone knows differently, please correct me. my experience is with the 1.6L which is DOHC**
i have had similar problems with an older car. for me, there was a small pit out of one of the cam lobes that did not affect the car or reliability at all - it simply made some slight valve noise at around 5500-6000rpms.
so there are some possible problems:
- same as above, damage to a cam lobe. remove valve cover and inspect visually.
- cam lobes worn and out of spec, you'd need to remove the camshaft and take a micrometer to the lobes to check this. see Hyundai Service Website
for the specs.
- clogged hydraulic passageway in a rocker, then the lash adjustment isn't possible. would require replacement, but for the cost i wouldn't worry about it. not going to damage the engine in any way. dodge neons are famous for this crap.
- timing belt wearing out and then at certain RPM's the timing slips a little bit. belt could be stretched/worn or a pulley could be going such as the tensioner pulley. simply remove the top half of the cover and inspect visually with a good flashlight and inspection mirror. if the T-belt has never been done, you may want to do this anyways.