At the beginning of every session, announce which character your character trusts the least; their player will spotlight a Faction for your character (that isn’t already marked).
Mark that Faction.
Tell the MC about a rumor or conflict that you’ve heard about that Faction, building on previous established information if you’d like, and roll with the Faction. On a 10+, you’re prepared for the conflict you laid out: you’ve got a Debt on someone in that Faction or a useful piece of information or equipment, your choice. On a 7-9, you’re neck deep in it: you owe someone in that Faction a Debt, and someone in that Faction owes a Debt to you. On a miss, you’re caught flat-footed, unprepared, or unaware: the MC will tell you who is coming at you.
Considering how Kimi's Debt to January is written, and her profession as a forensic auditor, I would say she would trust January the least.
With her profession in finance, she definitely would have encountered people who used tactics like January's to get others indebted to them. Plus, with how the deal he offered is phrased, she is naturally cautious. Doing any favor he asks for in the future sounds like giving him a signed blank check...
I think during the meeting with January to establish the deal, she may have realized that January purposefully had information about him sent to her purposefully and indirectly. She would have taken the deal cautiously, express that whatever favor she owed January would not endanger the lives or livelihoods of herself and her friends during making that deal, and have the conversation recorded. With the recording, she would have a 'copy' of the verbal contract for reference, and hopefully make it harder for January to try anything funny.