I have found a bit more information on the topic.
In the webpage authored by National Astronomical Observatory of Japan   https://eco.mtk.nao.ac.jp/koyomi/wiki/BBFEB9EF2FB2C6BBFEB9EF.html , it mentioned that using Showa 23 (year 1948) as example, 13pm of September 11 in summer time will equal to 0am of September 12 in standard time.
It cited a document issued by the Liaison Office which briefly existed during the postwar period of Japan, where the detail on implementation of the summer time is described in the document. https://eco.mtk.nao.ac.jp/koyomi/wiki/BBFEB9EF2FB2C6BBFEB9EFB2C6BBFEB9EFA4CEBCC2BBDCA4CBA4C4A4A4A4C6.pdf 
The text in the document do instruct a fall back to occur at September 11, 13pm in summer time, while ordinary citizens can change the clock before they sleep.
* Note: despite the webpage being named as wiki, it is actually a collection of information maintained by the Ephemeris Computation Office, NAOJ, not something that can be edited by others.

2018-9-19 Wed 04:59, Paul Eggert <eggert@cs.ucla.edu> wrote:
On 9/18/18 1:43 PM, Paul Ganssle wrote:
> The law says that the last day of DST had 25 hours instead of 24. The
> question is whether in practice what happened was that starting 0:00 on
> Saturday, did people wait 25 hours (until 01:00 on Sunday) and THEN set
> their clocks back 1 hour, or did they wait 24 hours (until 00:00 on
> Sunday), and then set the clock back to 23:00?

Yes, that's the nub of the question. If people in Japan generally did
the former, we should change tzdb to model the transition as one from
01:00 to 00:00 Sunday; this is not exact but is the best we can do. If
people generally did the latter we're OK as-is. Possibly some people did
one thing while others did the other, as the American occupiers did not
always see eye-to-eye with the Japanese populace and I doubt whether
it's entirely a coincidence that Japan stopped observing DST three days
after US occupation ended.

As we've already mentioned, old Japanese-language newspapers could help
resolve this issue.