Not an astrophysicist, but I think the assumption is that all of the photons are emitted at once in an explosion, and of course they all travel at the same speed. So if the burst is two minutes long, the near side of the explosion was two light-minutes closer than the far side of the explosion.

Imagine observing a lightning bolt strike the ground. The bolt travels through air almost instantly and emits sound in every direction throughout its path. First you will hear the sound waves emitted from the point that it touches the ground, because that is the closest. Then you will hear the sound waves from 1 cm off the ground, 2 cm, 3 cm and so on all the way up to the lightning bolt's point of origin in the sky. By measuring the duration of the noise you can tell the length of the lightning bolt (assuming it's perpendicular to the ground).

The length of the burst tells us the maximum size of the event. Imagine the event takes place instantly at the source, and that the source has some size. If we observe the event over two minutes, then the event size was two light-minutes.

In reality, these aren't completely instantaneous events. But any event duration at its source is going to decrease the event size. Take the extreme case: the event actually took place at its source over the course of two minutes. And we observed it over two minutes. We would have to conclude that the event had zero size.

Of course, the reality is that we have no idea how long the event took place at its source. All we know is that we observed it over two minutes. But that's enough information to conclude that the event we're seeing certainly occurred within a two light-minute sphere. If it had occurred over a larger sphere, we would have observed it over a longer period of time because of the time light takes to traverse the length of the source.