Ok - what I kept myself from rambling in the tags is this:
In the very first timeline, Mami mentions wanting Madoka to be fully trained to fight Walpurgisnacht, and in the second timeline, she correctly identifies Homura’s magic as time magic, along with stating, “It’s incredible, but it’s tricky to learn how to fight with it.”
This leads me to two theories:
1) Mami’s witch and magic analysis has led her to be able to both accurately identify when and where a Walpurgisnact will show up based on local criteria (which doesn’t seem outside of her bounds, considering how quickly she is able to track and locate witches, not just using her soul gem but also through a general idea of where witches might be most attracted (as seen in ep. 2)) and know another magical girl’s magic through one use (again, not outside her bounds, given her identification of not just Kyouko’s magical ability but also the magical ability of the witch Kyouko was fighting when they met in The Different Story). This theory relies a lot on Mami’s previous experiences and intellect, which, given my previous headcanon that she’s been doing this for two years, the above notations that these are not outside her bounds, and that Mami is the sort of person who teaches and studies until she is able to do what she wants (creating muskets out of ribbons, making tea just appear out of nowhere, teaching herself healing powers (as seen in ep. one with Kyubey) even though all of the above is outside of her initial magical powerset), it isn’t too far out of bounds.
2) Oriko and Kirika, considered an anomaly in the Oriko timeline, were not in of themselves the anomalies. It is possible that Mami knows - or has been in touch with - both magical girls prior to the first timeline. Oriko could easily have seen Walpurgisnact and worked to get magical girls to defeat it (not likely, given that we only see Mami and Madoka fighting the witch at the end of the first timeline), and Kirika’s time magic would give Mami a base knowledge to work off of in regards to Homura’s magic. The anomaly, then, in the Oriko timeline is not that either Oriko or Kirika are magical girls, but the form they function in that timeline (Oriko seeing Kriemhild Gretchen and using Kirika to mass murder magical girls in an attempt to save the world), which seems more than possible to me. This theory relies less on Mami’s mind and more on her social graces, which also makes sense. Mami is known to help other magical girls fight witches, even when they seem to be losing (again, the two girls she saved in the beginning of The Different Story, and Kyouko herself, on their first meeting), and she constantly wants a partner with whom she might fight witches. This latter is a strike against this theory, however, as if Oriko and Kirika were teaming up and Mami knew about it, why wouldn’t they include her on their team?
...so, for the most part, I side with the first theory and want to remind everyone that Mami is brilliant, in case you didn’t know.