A refreshable PDB clone is associated with a PDB-specific logical timestamp (LT) service that continuously reflects the LT of the most recent changes that have fully committed within the PDB clone during a refresh operation. Such an LT service is used to perform queries over the changing data in the PDB clone while the PDB clone is undergoing a refresh operation. Furthermore, a PDB-specific LT service can facilitate write operations in a standby CDB, where the standby CDB is a physical standby of a source CDB. Specifically, a standby CDB is configured with a private read-write PDB that does not replicate data from the source CDB. This private PDB may accommodate a write operation required by a query over data in the standby CDB. A PDB-specific LT service provides LTs for such a private PDB where the PDB-specific LT service provides LTs to order changes made within the private PDB.