Before measurement it's one detector, then it interacts with half photon, which is superposition |photon>+|no photon>, and the detector's state splits, the first state interacts with the |photon> state and measures it, nothing happens to the second state, because there's nothing to measure in the |no photon> state, but the first state splits away from the second state and leaves it alone, that's how the second state ends up alone with pure |no photon> state, but this really was done to it by the first state, the second state can't do it by itself. For this to happen in the second branch you need measurement to happen in the first branch, so when you are in the second branch, the first branch still needs to exist even though you don't see it, otherwise your branch won't be able to be as it is.

When you remove detector and start next measurement, you start with your one branch, branches from previous measurements don't affect it, the phenomenon happens during decoherence, nothing happens after it.

Your article explains this with branching without saying the word.