What's this tense called: "I been done ate"?

In Wikipedia and this article by Joan Fickett, it makes the distinction between recent past and pre-recent past:

Recent:

She done work.

Pre-recent:

I been seen him.

Edit: Still trying to figure out the name for the "been done" + verb tense, which is yet another tense/aspect that doesn't exist in Standard English.

This seems a lot like where I might say "I have been done eating for quite some time now." Sounds the same tense with just the "have" omitted and the action verb cast to the past tense.