There are correct ways these days. Japan largely uses the Hepburn System of Romaji. China uses the standardized Pin Yin System.

However it is true that such systems were in a state of flux in the early 20th century. China did not adopt Pin Yin as a standardized romanization until after the Communists won the civil war post-WWII. Before the CCP standardized China had several competing romanization systems including the infamous Wade-Giles system which was terribly inaccurate for Mandarin (Beijing --> Peking) since it was based around China's southern dialects.

Japan's romanization system was constantly being developed until a general consensus formed around the middle of the 20th century.

In fact English was not properly settled until the middle of the 19th century. If you read documents such as the US Constitution you will get interesting language nuggets like this:

The Senate shall chuse their other Officers, and also a President pro tempore, in the Absence of the Vice President, or when he shall exercise the Office of President of the United States.

And random capitalization of letters like this:

To raise and support Armies, but no Appropriation of Money to that Use shall be for a longer Term than two Years