This time leap function better be explained because the more characters it adds, I fear its going to be used as a continous device for conflict in the story. For clarification, I got no issue with the way characters been used by it so far.
"Hey, don'cha remember me? I'm your long lost best friend from so-so company so let me be part of your life and live in your house. Because we're friends and that's what friends do! Did I mention you never changed? Hahaha" - some trustworthy stranger
You could have gone to a restaurant and talk things a bit, why do these two had to sperg out this bad? They're supposed to come from a more civilized era...
This is really out of character for Ken to just straight up refuse without judging the situation first...
He stayed quiet and then refused just to create a villain from his time line cuz the author demand it not how Ken the character shouldve acted...
Hope this wont turn into some weird drama ...