Just need a quick answer to clear this up.

I understand that you read out the appropriate epilogue at the end of each mission, but I’m unclear about the rewards.

Let’s say that the Rebels just won the Canyon Run mission:

Counterparts + the rewards under the epilogue

Or

just the rewards under the epilogue?

Counterparts + the rewards under the epilogue as told by End of Mission rules.

You only ignore the Additional Rewards if playing the Twin Shadows minicampaign, and include them if play as a side mission.