Replicated tables are essentially stored as round robin tables then copied to the first distribution on each compute node. So when looking at the output from DBCC PDW_SHOWSPACEUSED you will see the data spread across all 60 distributions. You will see a few distributions (first distribution on each node) will have a greater amount of data stored. You can add WITH IGNORE_REPLICATED_TABLE_CACHE to the DBCC PDW_SHOWSPACEUSED command to show just the data space excluding the replicated copy size. What you are seeing is not that the data isn't being replicated, but just a byproduct of the way replicated tables are implemented.
There is a process that builds the replicated table cache that will show up in sys.dm_pdw_exec_requests with a command called BuildReplicatedTableCache. You can then see the status of the replicated table cache in the DMV sys.pdw_replicated_table_cache_state.
Additional information can be found in the documentation at Design guidance for using replicated tables in Synapse SQL pool.