Started a Core + Twin Shadows campaign as Imperial Player, took Inspiring Leadership class and bought Press On with my first XP. This lets you remove one damage from all "figures in an Imperial group" at the end of a round. I interpreted the use of the term "Imperial group" to refer to those groups with deployment cards having the Imperial faction symbol on the card back, so Officers, Stormtroopers, Probe Droids, etc.

First side mission is Spice Job. Heroes must retrieve a key card to open a room containing Spice and boost it from the Hutts. Key card is one (yellow) of three (the other two are red) Neutral mission tokens that are randomized and placed under a Probe Droid (Imperial faction) and two Elite Transdoshan Hunters (Scum faction). But the rules for Spice Job state that the players can retrieve the token once the "Imperial figure" it is under has been defeated.

So could I have used Press On to heal my Scum units, not just my Imperial units?

In the campaign, all figures under control of the Imperial player are Imperials, regardless of Imperial or Scum faction on the card itself.

In the campaign, all figures under control of the Imperial player are Imperials, regardless of Imperial or Scum faction on the card itself.

Yup that's correct.

Note that there are times where a card or rule is specific to a faction, but in that case the rule text will show the faction SYMBOL, rather than refer to Imperial or Scum. For example the "By Any Means Necesssary" Agenda card from the "Soldiers for Hire" Agenda set:

http://cards.boardwars.eu/index.php?album=Ally-and-Villain-Packs/Wave-2/Boba%20Fett/Agenda%20Deckℑ=By+Any+Means+Necessary.jpg

Thanks, everyone.