Situation:

My opponent has Jorah's Cohorts (Response: After you win a Power challenge, choose and discard an attachment from play) and one of my characters has an attachment that I would like to discard. I've won Power Challenge by 4 or more and use Seductive Promise (Response: After you win a Power challenge by 4 or more total STR, choose a non-unique character controlled by the losing opponent. Take control of that character) to take contol of Jorah's Cohorts.

Question -- may I use Response of Jorah's Cohorts immediately, for winning Power Challenge, in which I took control of it?

Sure. The Response window is still open, and once you take control of the Cohorts, you can trigger their response.