Postdoc position not specifying about required recommendation letters
While it seems unusual, I'm going to guess that he knows what he wants and needs. I wouldn't send things that aren't asked for in this case, as you seem to have already made it over the line. An accidental statement in a letter might actually hurt you, but I don't see how you can be "more" accepted than accepted. 

If asked, send them of course. But you will likely learn more at the interview. 

Depending on his funding, he may have wide latitude in who to hire and how to do it.