It's the investment accelerator. Monetary tightening means lower expected NGDP; real interest rates can go either way. Think of this as a teaching post, to explain the intuition. Or look at Miles Kimball's great post.
Here's a thought-experiment. Do not take this thought-experiment literally. It's just my weird way of doing the math, where I start with the answer and work back to the question it answers. Sometimes it's easier this way. Like trying to figure out the relationship between policy X and outcome Y when you know that Y/2=X but you are really bad at algebra so you can't solve for Y=2X.
Imagine that expectations are totally non-rational. Expectations are just exogenous, and do not adjust to match what is actually happening. And one day everyone wakes up expecting a permanent recession. When they went to bed they expected that output would remain at 100 forever, and nothing would ever change. Now they expect that output will be 90 forever. A permanent 10% drop in output.
But the central banker is an New Keynesian macroeconomist who years ago made a bet with his grad skool classmates that expectations are rational. He has since learned that expectations are totally non-rational and exogenous, but he doesn't want to lose his bet. So he has to figure out a way to make the world adjust to match the expectations people hold, since the expectations people hold do not adjust to match the world.
So what does the central banker need to do to the real interest rate to make those non-rational expectations of a permanent recession look like a rational expectations equilibrium? (Remember, I'm just solving for the New Keynesian equilibrium in a weird way, to make the math easier.)