Recently finished this and after thinking about it for a while, I think Satoshi lied about the paper being his sister's.
If you go back and check, his sister didn't even participate in the ritual. And it was pretty weird that Satoshi gave Naomi his own paper instead of just giving her the extra charm. So the only explanation that makes sense is that Satoshi lied in order to bring Naomi Nakashima back safely while knowingly putting himself in jeopardy.
Satoshi gave Naomi his own charm to bring her back safely but maybe it wasn't such a selfless motive. He knew he couldn't live on in the real world again with the memory of his tortured little sister dying in his arms after stupidly leaving her behind alone with the girl with the red dress. We all saw the effect all of these memories had with Naomi, after she survived, she basically went insane.
(Note: In the Corpse Party game it's revealed that anyone that dies in the elementary school, memories of them are completely wiped out in the real world having them be completely forgotten by their loved ones)
Also worthy of noting, the ending when Naomi's mom is talking to her doctor about how Naomi keeps talking about "her friend" and how "she" doesn't exist brings us back to the scene of Naomi killing her best friend (Seiko Shinohara) while seemingly possessed. For Naomi, being one of the only survivors in her group of friends, and not to mention killing and watching her her best friend die drove her to insanity.