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That is a good question. To be clear, Jerry does not seem to be muddled up or confused, but he did reach a possibly inaccurate conclusion based on incomplete information. That's probably a little unusual among immortals, honestly.
Too soon to have any faith in an alternate universe theory, in my opinion.

Jerry can sense a very real connection between Susan and Diane. So close it leads him to believe they are sisters. What if he is sensing something so similar as to be almost identical between them that he is getting confused. Would be easy for him to be muddled up in what he feels seeing as he has not long reset himself.
Could Diane be Susan? To be exact, Susan from another dimension? Maybe her parents crossed realities, gave birth to Diane and then something happened to them, or they left her there in hopes of a better life for her?
 

This may be the most painful page of EGS that I have read in quite a while. I don't think I have seen anything even near it since the time Tedd acknowledged Mr. Verres' transphobia.
It is clear that Susan has held a mental image of her father close in which she tried to preserve at least some sort of person worthy of love. It would be easier to think of him as someone who started with good intentions but stumbled into a bad mistake. Being brought face to face with the possibility that not even this much was true... yes, anger and denial are two of the first steps. Having it all intermixed with her immensely traumatic experience with the vampire back in France would not make it any better, to put it mildly.
I am torn. Nanase unquestionably meant well. But I am starting to think that she would have done better to think this more carefully through. Even so, I am doing this from hindsight so I am not precisely in a position to criticise her. Her intentions are obviously good and based on the fact that not only is Diane in danger, she also deserves to know of her half-sister's existence... and that Susan deserves to know the truth as well.
The problem with that is that while truth indeed has the power to set you free, it can also open old wounds and do grave harm. It is for that very reason that Ellen rejected the notion of telling Tedd what they had learned about his mother. This situation is of similar complexity and may well reopen old wounds for Susan... and possibly even make them worse.

At this point, even if they're not related, it isn't just about birth. The sister you make along the way matters as well, just ask Elliot.

I certainly didn't mean to do that!  It may not be the rapid hair growth on its own, but I'm highly suspicious that Akiko is well aware that Nanase can do magic, so if she did realize it was magic, she probably just thought her big sister was especially cool when it happened.  Little kids are good at telling when something is a secret, and Akiko is smart enough to get that Nanase doesn't want Mom to know about her magic.  Only real question is whether Akiko has or will overhear Mom talking with someone else about Nanase's magic, or otherwise find out that Mom knows more than she lets on.

We've already seen Akiko manifest Cookie Fairy powers.

The story remains coherent. To include such a detail is not unreasonable.