We have hired a tour guide to take us through Pompeii and Herculaneum. I need to prebook tickets. We are traveling with 18- and 20-year-old kids. So quick question it looks like the reduced rate for college age kids is only for EU citizens and child rate, if I am translating correctly, is for under 18. So purchase 4 adults, correct?
Yes, your 18 year-old and 20 year-old are considered adults.
While I know that it's sometimes possible to find other shades of meaning by translating an original-language site, didn't you have a drop-down Choice of Language at the top-right of your page? One reason I ask is for fear of your being on a third-party site, instead of the official seller.
https://pompeiisites.org/en/visiting-info/timetables-and-tickets/