reader connection stays open until the reader is closed.  Writer connection is acquired for each chunk at the time of committing the chunk, and is closed after the current chunk is done.

If reader and writer connections are obtained from the same datasource (by the same jndi name), it means they are from the same connection pool.  But there should be no interferece between the two.  Since the reader keeps its connection, so the writer will not get the same connection as the reader.