So, the stuff inside the balloon that makes the web is called HI-FLOAT, and it’s a commercial product actually sold for injecting into helium balloons to make them retain their helium longer. It forms a skin on the inside of the balloon and keeps the helium from diffusing out so quickly.
The “web” effect is created by applying the HI-FLOAT and letting it dry at one pressure, and then deflating the balloon, stressing it, and then re-inflating to a higher pressure, causing the film to detach from the walls (which, of course, means it’s not working as a sealant anymore, but whatevs).
I’m pretty sure this trick was developed in-house, by the company that makes it, to sell more HI-FLOAT. Still, it’s pretty cool.