As shown in the Ep.0 manga, whether or not [Persona] exists, Matoi was on the verge of become the [Profound Darkness] at that moment because of all the darker energy she had absorbed up to that point in her life; her being sent back in time is the result of Clarissa's/Xion's attempt at purifying her.
Xiao's and the Player's intervention merely caused things to play out in a slightly different manner - Matoi bonded with the Player as opposed to Melphonsina - but everything else essentially was already destined to happen.
In the Ep.0 timeline, the purification process kills Shiina, but in ours, Xiao pulls us back before it can do the same to the Player. So although it seems like Xiao pulling the Player back also pulled Matoi back, they are merely two separate events that occurred simultaneously.
Matoi's memory being erased is the result of the forced purification, as far as I can tell, and Xion erased knowledge of Matoi to be able to protect her from Luther for when she could be rescued.
I'm assuming the kin line relates to the fact that she was connected to her through Clarissa, but I may be wrong there.
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