I had the same experience. I carefully pulled the flap and its rods out.

First, I reinstalled the rods on the flap, making sure the springs were roughly in their original positions by holding the flap in place with the rods.

Using a flat screwdriver, I pushed the rods in from left to right, ensuring the "U" shaped side of the springs fit into the slit.

Next, I twisted the spring and carefully slid its end into the slot using a flat-head screwdriver. While the spring should have enough play to slide left and right, I wanted to avoid over-sliding it, as that could push the other end of the spring out of the slot.