[i mean he'll take it if offered but sentimental attachment is...a bit beyond him]

It's not all that unprecedented. The concept of parallel worlds and timelines is a known facet of magic, if the sort considered 'so rare as to require a miracle'. I'm not fully certain if it's that at work, a mere timeline discrepancy, or a bizarre combination of the two.

As for Rin, she also recognizes 'Kirei Kotomine' as someone else. It's a bit more complicated than I am truly able to speak upon.