Just where tile quilts fit into the history of quilts is a matter of speculation. One suggestion is that they are precursors of crazy quilts; another idea is that they represent an offshoot of broderie perse (cut-out chintz images appliqued onto another background). I would guess there is some truth to both theories.
For more information on traditional tile quilts, see the first chapter of Tile Quilt Revival: Reinventing a Forgotten Form by Bobbi Finley and me. It is "A Brief History of Tile Quilts," which pictures and describes tile quilts from several private collections as well as the collections of the Shelburne Museum, International Quilt Study Center, The Abby Aldrich Rockefeller Folk Art Museum, and The New England Quilt Museum.