Hello, great question.
The picture you have included in your post is an homage to the 3646, made by Rolex for Panerai. It was a very large watch 47mm with a long strap. At the time, the Italian frogmen who used these timepieces could strap them to their leg while sitting on top of their manned torpedo submarines. Because it was dark and water probably murky, it would have been easy to become disoriented, and did you strap the watch to your leg with 12 o’clock pointing towards you or away? Thus having a watch that was easy to tell where 12’clock was was essential. A dial with Roman numerals on the top half was created and called “error proof”.
In the 1930’s Rolex began producing a very popular watch, the Rolex Perpetual, or bubble back. They came with various dial designs, some of which featured the “error proof” dial.
After WWII the Japanese government stimulated their economy to encourage regrowth and many Japanese citizens suddenly had money to spend. One item of popularity was the Rolex bubble back, in particular with the error proof dial. Japanese vintage watch dealers quickly ran out of these watches so they looked to the US market. Soon they ran dry as well, so a California based dial refinishing company, Kurt Rich Dial Corp. began to reprint standard bubble back watch dials with the “error proof” dial. These refurbished dials became known as California dials because of where they originated.
So no, the dials never have said California on them, they are just a nickname.
Here is a California dial from my collection:
