I’m using the premium version. I looked in the code and from what I can tell, for a Drupal 6 import, only a single attachment field is created via Pods (none of the custom field tables are ever queried). So, I just wrote my own scripts to handle the custom data after the import runs. It’s not the best solution, but it works for our use case.
Just to clarify, this a Drupal 6 system with 5-6 custom content types with 4 of those having custom fields (all of type text).