What was Martina and his family in "Picking up the Pieces" by Pat Cadigan?

I just read the short story "Picking up the Pieces" by Pat Cadigan and despite reading the bit where the first person character sees Quinn and Martin and his family I still did not get what was happening. It says things like the rational part of my mind did not believe and Quinn says something along the lines "you saw didn't you?".

The only revelation about Martin and his family is that

So I don't know if I skipped over the important revelation in both readings, if it was too obscure for me or if I need to be familiar with some other works but can someone tell me what was the deal with Martin and (presumably) his family?