I intended for Alpha Proxima II to be just what I said it was in the text, and I appreciate foravalon
actually, y'know, using the text
So yes, they're Federation members (if they weren't, Decker and Kirk wouldn't have had the authority to declare martial law), and no, they're not part of Alpha Centauri.
Which leaves the name of their system rather inexplicable. It means "First Closest."
Oh well, at least it isn't something like Alpha Omicron or Delta Theta. Those are more like sorority names than star names.