I suppose this would be most easily asked with a little story.
Two people are on a ship, one from Faction A, Sam, and one from Faction B, Bob. Sam and Bob are not getting along, and the ship is in a system/sector Faction A controls, so Sam decides to A/E Bob. However, Bob manages to get the ship into hyperspace before Sam can accomplish his deed, with the destination being space that Faction B controls. Can either of these two A/E while in hyper or does Bob need to wait until the ship arrives?
I'm pretty sure you can't AE in hyper. There may be an exception if it's a capital ship belonging to Faction A. In which case getting into Faction B's territory won't do them much good anyway.
And it also relies upon both A and B being governments, as otherwise their faction controlling the territory is irrelevant.
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"May the Grace of Ara go with you, and His Vengeance be wrought upon your enemies."
I remember items giving a location in HS, so up to now I was under the impression that you still have a location (technically spoken) while traveling through hyper. So if you're passing through a sector controlled by a government in a non-cap ship, these gov has A/E privs on your ship. I might be wrong, though, never tried it...