Well even if that is the case his sentiment of wanting her to look at this him is still valid. He may be Atsuhito's reincarnation but that also means he is not just directly Atsuhito. He's a different person with different memories, and even potential for a wholely different personality.
Being a "reincarnation" seems like a one-to-one for those outside looking in (especially with how it is most often portrayed in these kinds of stories) but really you are not your past lives, not fully. You are a new person living a new life. It's more like an old job you once had and you're working another job now but instead every aspect of who you are. You used to be A, you are now B. You are no longer A. B is their own person separate from A. However your life as A life may have taught B some subconscious lessons that help you.
IMO what you described isn't really a reincarnation, and closest thing i can think of would be something along the lines of remembering memories of your ancestors/blood memory/genetic memory.
In what i consider reincarnation there's no person A and B - there's only person A, you just don't know that B was actually only a subset of A all along.
Suddenly regaining memories from your past life is the same as suddenly remembering something from your early childhood, or regaining your memories after suffering amnesia. Doesn't matter if you remember your whole life, or only some aspects - they are your own memories.
And well for me if we go even remotely into 2 souls in one body/mergers then i consider that possession.