From what I can tell it generally goes by regular season record/standings during the regular season. In the preseason it goes by your previous regular season record/standings. If you claim multiple players there is definitely a system in place to allow only one player claimed per waiver process until all teams are finished as I have been burned by that process getting a not so good player instead of a stud before.
You had no other claims, had the worse regular season record, and still lost the waiver claim somehow. This is not verifiable, but my current hypothesis is that the playoffs might use some other waiver claim system than the regular season similar to the preseason. What factors affected it unfortunately, I have no clue. You do have a regular season win over Cincy this season but you are a full win behind still.
My other hypothesis is that waivers do not reset each week, like literally every other waiver system I have seen which btw this is literally clown **** we have no official documentation about how waivers work, and so your claim in week 15 put you behind Cincy since their week 15 claim was denied and neither of you claimed another player before this past sim.
Doomsday hypothesis for fun, playoff waivers use preseason waivers where LAST season's record is the playoff waiver each week which actually would explain this phenomena. But correlation != causation and I have no proof of this being the case.