Are there no lingering effects when you draw these cards?

What cards? Whish I could help, but I don't get your question. All Mythos consist of two parts, as described on pag 15 of the revised rulebook: an Immediate Effect and a Lingering Effect.

The Mythos Insight cards are in the expansion pack. There's a question mark and two arrows in the middle - one pointing up and one pointing down. You're supposed to choose one. It says, "Immediately after the players choose, the chosen option takes effect." So I'm assuming the other one doesn't happen, and that there is therefore no lingering effect?

Uh, right, sorry, they arrived with Unseen Forces. Yes, in this case there is no lingering effect: you simply decide which part of the Mythos to resolve