I suspect there has been some miscommunication.I imagine they will measure you, and fit you on their fitting coat, which is a sleeveless jacket that is pinned. I suspect then that they will deliver you a finished suit. I doubt that they will cut your fabric and baste it together for you in the same day you are measured.
You can get chest canvas if you want something more traditional. My coat has a chest canvas. Orazio Luciano also have much wider access to fabrics than the Danish PJ workshop. Holland & Sherry, Lesser, JJ Minnis, Ariston, etc. I ordered something from the JJ Minnis Fresco II Book.