Readers are read in depending on the order they appear in the Navigator window. From top to bottom. You can either right click and select Move Up or Move Down or drag and drop to reorder them.

To write data out and read back in use FeatureWriters and FeatureReaders rather than normal Writers and Readers.

I agree with @Gary Nicholson​, if the order in which readers and writers happen is important you're going to want to use FeatureReaders and FeatureWriters. The SQLCreator and SQLExecutor might come in handy too.

Thanks for your answers. However I have still two questions:

1) I can, indeed, reorder the Readers and Writers, however, I have one single Writer to a postgreSQL-connection so far, writing out data to different tables. But anyhow I cannot order the order of these different tables within this one Writer

2) How can I write out data and read it back immediately using the FeatureWriter and/or FeatureReader?

1) When faced with this I usually create multiple writers even though they are the same format. There are some tricks using Creators/FeatureMergers/FeatureHolders that allow you control when things are written as well.

2) But Feature Writers and Readers can give more control. If you need to read data back in after writing then do this

3) I agree with @Hans van der Maarel​ the SQLExecutor is worth looking at with PostgreSQL.