The crawl from the campaign book references Yavin after the DS is destroyed. How is it that the empire has outposts all over Yavin? Or am I missing something about the setting of the core set campaign?

I could be wrong, but I believe that the text on the mission says it's a "nearby" outpost. Technically, I guess that could be an entirely different planet/moon in the system, broadcasting info from the battle. Or, I guess it could be a strike team launched on the moon's surface, setting up show in a secured Rebel outpost or old Massai ruins.

The first mission takes place at an outpost near the Rebel base - but yeah, it's not specific as to whether it's 'nearby' in an intergalactic sense, or actually located on the planet/system.

After that, the next story mission takes places at an unspecific planet, but it's intended to be somewhere else. From memory most of the missions are meant to be on random, unnamed planets.

If I recall correctly...

I'm too lazy to look it up right now, but I think the plot of Aftermath goes something like this: The Rebels are evacuating Yavin 4, but some Imperials have taken over a Rebel outpost with some sensitive information. So you as the four Rebel heroes have to bust back into your own outpost and get the info before the Imperials do.