It is up to WordPress to determine which template to use upon redirection. I'm not too experience with template hierarchy and such, but I believe it depends on which query variables are set. A possible workaround could be perhaps to make an if statement on the top of the page.php file to include the correct template file. There might be a better solution though, I'm not sure, it is a template and permalink related issue – which I'm not experienced with.
Best,Ernest Marcinko
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