My question essentially is does a location card need to be in play when the triggering condition occurs to use its reaction in the reaction window.

My reading of RRG leads me to believe there is no such requirement,

The reason I ask is, the way i read it, you can win a power challenge by 5, then reaction window opens, you play the upcoming card, Supporting the People, search for The Mander. The reaction window is still open so you can kneel The Mander to draw 2 cards.

Am I right?

You can do that. The requirement is that the card is present at the time you trigger it , which means it can enter play (or you can draw it) during the relevant reaction (or interrupt) window.