How does MOVE COMPRESS affect future data?
Your DBA was kind of correct, for the typical scenario.

MOVE COMPRESS compresses existing data with Basic compression.
Any new data inserted with regular insert will be uncompressed. New data inserted with direct-path insert will be compressed.

If you want all new data to be compressed, then you can use OLTP compression. Then syntax for that is COMPRESS FOR OLTP. OLTP compression requires extra license as it is part of the Advanced Compression option.