Star Wars: Aftermath takes place after the events of Return of the Jedi.
Luke and Wedge were both present for the briefing before the Battle of Endor:
Antilles was present at a briefing aboard the Rebel command ship, Home One, in which High Command introduced the plan to destroy the shield generator protecting the Empire's second Death Star
Since Luke and Wedge were both present for the briefing before the battle, it makes sense for both Luke and wedge to also be present for the debriefing that occurred after the battle of Endor.
Luke Skywalker, a Commander for the Rebel Alliance, would have reported to High Command in that post-battle debriefing. That report would likely have included the revelation that Palpatine was a Sith. Knowing the Sith identities of Emperor Palpatine and Darth Vader, it wouldn't be too difficult for Wedge to work out how Palpatine's scheme had unfolded in hindsight.
Even Tarkin, without knowing (for sure) that Palpatine was a Sith, had suspected the Emperor of having orchestrated and manipulated events in his favor during the Clone Wars and the Galactic Civil War.
The "seeds of the Empire" that came from around the Outer Rim include:
Emperor Palpatine was the senator of his home planet Naboo, which is right on the border of the Outer Rim
Darth Vader was born on Tatooine
The Clone Army that would obey Palpatine's orders with out question were created on Kamino
The droid armies that gave Palpatine an excuse to use the Clone Army were built on Geonosis
Wedge would know about these things as they were generally known historical events.
So in conclusion, Wedge would've known about how the Clone Wars led up to the creation of the Empire and would know Paplatine was a Sith after Luke filled everyone in after the Battle of Endor.