Regardless of the time of day you decide to fly, the ticket price will remain around the same. Book flights from Kagoshima to Manila as you normally would.
These are just IATA (International Air Transport Association) codes. They are used in aviation to identify and differentiate airports. That’s why a Kagoshima Airport to Manila Ninoy Aquino Intl Airport flight would often be abbreviated as a KOJ to MNL flight.