I'd say they started getting into their swing in the 1950s, if my father's Yashica-A twin-lens reflex is any indication. That camera produced absolutely gorgeous shots in square format on 120 roll film.
I own some several Japanese medium format and love the photos they take.
I seem to recall that ergonomically it was a bit iffy too, but that may have just been the fact that I was more familiar with the Yashica.