Rendered File field in view doesn't use custom formatter

I created a custom formatter (a D7 port of the PDF Preview module) and it works well in nodes. However, the Rendered File field in a view doesn't use this formatter, even though I changed the file display settings (e. g. in dmin/config/media/file-types/manage/application/file-display) for the "Application" and the "Other" file types (see screenshots attached).

How can I make the Rendered File field using my custom formatter for PDF files?