As of CUBRID 8.4.0, it does not support timezone. Currently it follows the system timezone.
So users migrating their data, for example, from Oracle or PostgreSQL should remember that if they have data in TIMESTAMP WITH LOCAL TIME ZONE type, the timezone part of that data may be lost, only keeping the DATETIME information. See CUBRID vs. MySQL vs. Oracle Data Type Mapping for more information.
Though, if you look at Reserved Words in CUBRID, you can notice that TIMEZONE_HOUR, TIMEZONE_MINUTE keywords are reserved. This gives a hint that in the future versions CUBRID may support this feature.