OK. I removed all the custom code provided by BOTH you and Minesh.
The problem, as described, still exists.
So perhaps this is an issue with Views + WPML integration?
One curious point to note:
The problem only occurs when moving languages away from the WPML "default" language.
e.g. If we reverse the order;
1. Search on Japanese
2. Click on the "English" language switcher
3. Do another search
The results are correctly returned in English (the default lang.)
I have some content whose original language is English, with translations of each of the posts (in my case, to Spanish).
I created a View with a text search to search the post titles.
I inserted that View on an English page, and then translated the page, including the same View on the translated page.
In a different browser where I'm not logged in I visited the search page in English and performed a search. English results were shown.
I used the language switcher to swap to the second language.
The page updates and shows the unfiltered Spanish posts.
I perform a text search for the titles and Spanish posts are returned, as expected.
I noticed that you display the results on a different page from the initial search and modified my own set up accordingly, but still couldn't reproduce the problem.
I think I'll need to take a look at your site to see if I can identify the issue, and if needs be take a copy for further analysis.
I will mark your next reply as private so that I can get log-in credentials from you—you may want to create a temporary admin user for me to use that you can later delete. And be sure to have a current backup of your site, even though I don't intend to make any changes other than possibly to temporarily add a backup plugin to take a snapshot of the site.