Okay, so, I've defined a Numeric Variable: {Application.Variables.MySequence} (set to 0, increment by 1), which I used in the App "Attribute Importer" to fill a "Frame.CurrentFrame" attribute. This seems to get the job done, however, do I have to always set this variable back to 0 before I use the importer to fill an attribute with incrementing values, with respect to the files processed?
Yes. Auto-increment variables are incremented whenever you use them. That's their purpose. It's a very near concept.