The balloons are popped with a home-made blowdart made from a Q-tip and a pin.
The photographs are taken with a rig made from an Arduino microcontroller and a set of sensors and triggers.
The blowdart trips a photocell trigger as it exits the straw. That opens the camera shutter and turns off the room lights.
When the ballon pops a piezoelectric vibration sensor on the balloon sends a signal to the Arduino, which then fires the flash, closes the camera shutter, turns the room lights back on, and re-arms the system for the next shot.
This is very intriguing. What a clever set up. I have no idea how you do it even after reading your explanation. Anyway it is quite a way to capture a picture.