What does this mean in this context で、幽が引っ張っていくオチか >> So she is the one pulling the punch line?

Question

context is You (MC-as Kensuke in this dialogue) is speaking with 2 subordinate of a general /shogun (一葉 Kazuha) about her strange behavior recently (Hifumi and Koi)They're secretly following Kazuha and her subordinate (幽) Yuu

Hifumi......確かにそれは、公方様にしては珍しい

相変わらず一葉たちに気取られない距離を取って尾行しつつ.俺の話を聞いたーニ三は、ふむ、と小さな声を上げてみせた。

Kensuke : 俺がいない時の一葉って、どんな感じなの?

Koi: 私たちが京にいる間だけの話ですが……剣丞さまがいらっしゃる時と変わらないと思いますよ。剣丞さまの所が双葉さまか、久遠さまに変わるだけで

Kensuke:で、幽が引っ張っていくオチか >> This is the part I don't understand ( my guess is "So she (Yuu) is the one who's pulling the punchline ?>)

Hifumi: まあ、公方さまにあそこまで出来る方なんてそうそういないだろうしね

If you can please show me your English TL at the part I don't understand thanks .I don't know my guess about the punch line is correct or not

Answer 1

This オチ is "(unfavorable but easily expected) outcome" rather than "punchline". In particular, ～のがオチだ is a common set phrase that means "Surely it'll end up (something bad)" or "(Something bad) is all you can expect". See the second definition here, and the following monolingual dictionary definition.

落ち

３ 行き着くところ。結末。

㋐落語などで、しゃれや語呂合わせなどで話の終わりを締めくくる部分。下げ。また、一般に、話の効果的な結末。「この話には落ちがついている」
㋑物事について予想されるよくない成り行き。「断られるのが落ちだ」

Thus:

で、幽が引っ張っていくオチか
So, the result is that Yū takes the lead, huh?
And it (always) ends up with Yū taking the lead, huh?

(I'm not 100% certain about the meaning of this 引っ張る, so please change that part according to the context. It could mean "to (physically) drag her out" or something.)