>>93135006She's not doing that in these. This 'assassin geisha Ashi' AU comics all run with the assumption that past!Ashi does not even know about future!Ashi.
The fanfic that got mentioned up-thread has Jack do the obvious thing and talk about this when she expresses her confusion/fury (that Ashi goes for straight assassination...), but she never tries to use it as a lever against him, only expresses disbelief and discomfort with the idea (because both he and she are absolutely sure and absolutely adamant).
In the fanfic, anyway, it's implied that either Ashi was nabbed and brainwashed in the past through some means, or else she's somehow gaining memories of her past (well, future) self over time. I imagine the whole geisha AU will take a similar tack.