The fundamental question is why, if he was pro-Japanese, he went into exile in 1909. Not after the 30s, but in 1909. I think you are confusing (deliberately or not) being pro-Japanese in some fashion and being a Japanese puppet. As you must know, over many centuries the two basic political positions in Korea were pro-China and pro-Japan. Many thoughtful and patriotic Koreans were pro-Japanese in the sense that they thought that an alliance with Japan was the best way to develop. And in fact, before Japan went crazy with militarism, Korea benefited in many ways from the occupation, just as Japan benefited in many ways from the MacArthur occupation. You also refer to the "destruction of the titled nobility" by the Japanese. Did this really happen? The Korean royal family was sent to Japan and became Japanese princes. The old aristocracy pretty much stayed in place. Some of them were given Western-style titles, just as the Japanese created Western-style titles for its aristocracy, in order to co-opt them. The relationship between Japan and Korea is very complex, and is marked by both hostility and enmity and also feelings of brotherhood. The Japanese and Koreans are more closely related to each other ethnically than either group is to any other group in the world. The Japanese and Korean languages are related, and a speaker of one can easily learn the other. (That's why the South Koreans ban Japanese TV.) Hirohito's official policy was that the Japanese people and the Korean people were one race. (Kind of like the Romulans and Vulcans.) But in any case, who cares? Rhee is irrelevant in the present world, when it looks like the forces of communism and their friends have won the S. Korean pres election.
The Korean aristocracy was destroyed. The old titles of nobility abolished. In fact, the Japanese "terminated" their own titles of nobility in the 1920s (except for the royals, and those were substantially limited).
Koreans make a great deal out of having an equalitarian society (in terms of hereditary class).
To say the least the Korean people were "divided" when it came to the Japanese occupation, as were the Japanese themselves about Korea.
And no, they are not the same people. 40% of modern Japanese have a tooth type found only among the ancient Jomon and present day Ainu. The Shan Dynasty Chinese who fled Shan at the start of one or the other of our various Dark Ages who ended up in Korea on the South Coast moved on to Japan quite early and never mixed cultures with the later Mongol arrivals to Korea.
The Japanese royal family was recently found to descend from Korean invaders from the 500s.
It gets quite complex from there, but the two nations are more different than they are alike. There have also been many centuries of voluntary immigration into Japan from Korea. Japanese fishermen certainly established small villages on the coast of Korea. Both nations also went through periods of total rejection of the outside world with bouts of what can only be called "ethnic cleansing".
Politically, claims that both nations use cognate languages are considered a legacy of the Japanese militarist's excuses for the conquest of Korea. In reality, there are similarities - mostly in terms of vocabulary, like English and French, but the Polynesian grammatical elements in Japanese have no equivalent in Korean. In time English will supplant both languages, albeit an English without an "L" sound!
Still, you have to remember Mr. Rhee got started in 1897 demonstrating against YI. One doubts that he ever really changed his mind.