Bendis' post-Secret Wars run that began right after Miles joined 616 did. We even got to see his maternal grandmother, among a few other aspects. That said, prior, it wasn't too much of a factor beyond his mother Rio and The Morales family taking Rio's last name.
That said, I do recall hearing about that bio-electricity wielding spider before. That's actually pretty clever to base a powerset off of. This facet isn't really brought up in-canon or in fandom like it outta, though, so I admit to that reference to the source of Miles' powers still going over my head.