Yale was unable to react when he heard that kid's last words.
From the start, Yale had thought that the kid was a descendant of him from the future, but he never thought that the kid was himself in the past.
Although Yale didn't remember having been in the Timeless Border before, he knew that his past life had been there before and he still lacked a lot of memories, so it wasn't impossible for him believing that he could find his past shadow.
However, the white-hair kid was a real consciousness and not a shadow and meeting the real consciousness of his past was something that surpassed Yale's expectations by far.
"Are you serious?"
Yale knew the answer to that question, but he was unable to restrain himself from asking it.