In my experience it refers to development directly via SQL against the Postgres server rather than via an ORM like Django or the like. A remarkably high percentage of applications backed by Postgres have been written by developers that have never actually seen or written SQL code directly. It's all generated (often quite naively) by the object relational mapper. Requesting "native" developers means that they want you to understand how the DB actually behaves and to be able to generate optimal SQL code and proper DDLs that fit the application domain correctly.
When someone, e.g., as appeared in a recent and some older pgsql-jobs messages, says "Native Postgres", what do you suppose that means?
Does it mean something different than just "PostgreSQL"?
Likely it means the open source product built directly from the source code published here (or packages derived there-from). As opposed to say AWS RDS or EnterpriseDB or various other forks of the product available in the wild.