Asenath Downer (Cushman) - Alcessa Downer and Asenath Downer - two women or same person?

According to the book The Downers of America, by David R. Downer (published 1900), Alcessa Cushman was the first wife of Joseph Downer, and Asenath was his second wife. See page 56 of the scan of the book on Archive.org: https://archive.org/details/downersofamerica00down/page/56

That is the information on which I based the two entries for Alcessa and Asenath when I entered my geneological information on this site years ago. Later, someone merged the two women's entries into one. Is there primary source information verifying that Joseph only had one wife, and that her name was Alcessa Asenath (or Asenath Alcessa)?

I had re-added an entry for Alcessa, but then I thought I had better make further inquiries before adding any other detail, since the Downer history book I referenced is a secondary source, and perhaps the change was made from a primary source, and I wouldn't want to put in a lot of effort to change it, only to find out I was incorrect.

Can anyone shed any light?