You only choose either inflate or pop once at the beginning of each roll, but your bubble of dice carries over from roll to roll. So you need to kind of build momentum by getting a few small successes in a row before you can get to the bigger and bigger ones, taking on more risk each time you add one more die.
As for interpreting the prompt that starts things off, I left it deliberately vague about how exactly things went bad and what happened to Jamie so that you can interpret it as a group however you want.