I am to arrive on Airasia flight to HuaHin airport and going to the southern provinces. The trains seems to be not a good option because the earliest departure time direction South is after 5 pm. Minivans to Prachuap KK are not a good option either, too dangerous. I was looking for information about the buses but found nothing.

Is it correct, that Roong Reuang bus station serves northbound only? Where in HH is a bus station for southbound cities? Is there a terminal, where transit buses from Bangkok stop on the way to SuratThani, Phuket, or they pass HuaHin on route 39 off the city? Any suggestions how to reach Chumphon in the shortest time if landing at HuaHin Airport at 11 am ? 

If not on budget, Taxi is the best option. 

Lots of buses to the south. See https://en.wikivoyage.org/wiki/Hua_Hin