Sadly according to https://aws.amazon.com/dms/faqs/ https://aws.amazon.com/dms/faqs/ RDS SQL Server, RDS Postgres, and ODBC sources are supported in bulk extra

Sadly according to https://aws.amazon.com/dms/faqs/ https://aws.amazon.com/dms/faqs/ RDS SQL Server, RDS Postgres, and ODBC sources are supported in bulk extract mode only; the change data capture mode (CDC) is not yet supported. A shame since one of the biggest drawbacks to running postgres in RDS is getting the data out.