Yes. This name is definitely not "Native American." Ayana is indeed a name used in Ethiopia, but whether or not it means "beautiful flower" in any language used in Ethiopia has not been confirmed one way or the other.
And a very minor correction: I believe the person who runs the Native American languages site (at least the person who has corresponded with me through e-mail about it) is named
Laura Redish, and so is probably a "her", not a "him". :)