Just because the transports you are hitting are in Amarrian space, do not mean that the colony they are going to is as well.
In order to "pass back out" of something, you must have entered something. If they're passing back out into Empire border space, they therefore must have entered Republic space.
It was an observation that the hostile act on the capsuleers part consists of hitting a target outside 'their' empire's space. It's simply a fact by the game mechanic. Your mission will not be in "your" space, whatever the briefing says.
The logic is flawed there and I might simply chalk it down to the fact that the mission briefings might have been written before it was decided that FW missions always take you into hostile space.
So in a literal way, the mission briefing is not working at all. It claims that the amarrian fleet has entered republic space and is now detained there, waiting for a chance to get out again. However, the mission will send you to amarr space.
That's why I've said: Bend the story behind it so that it makes sense while retaining the gist of the matter, i.e. shades of grey, hitting civilians - or mostly civilians - it is.