In Star Wars: Imperial Assault, what information should be revealed to the Rebel players in the campaign?
Things the Rebels can know
The mission briefing

The Imperial player reads the “Mission Briefing” section of the mission’s rules aloud to all players.
— Rules Reference: Mission Setup

The full effect of any triggered events (both story text and effects)

Each event can contain any combination of story text and additional rules that apply to the mission. When an event is triggered, all of the text and rule information within that section is read aloud and resolved, in order.
— Campaign Guide: Mission Events

Note that mission effects are either instant (marked with a ▶) or ongoing (marked with a ◆). The non-italicized text after the mission briefing is almost always an event of this sort, so should be read out loud.
Rules referencing the mission ending or progressing (which are followed by the Rebel Alliance symbol)

Certain rules reference the mission ending or progressing, followed by the [Rebel Alliance] symbol. This indicates that the preceding text is an objective that the heroes are attempting to fulfill, which should be emphasized to the Rebel players by the Imperial player.
— Campaign Guide: Mission Events

Any previously stated rules

[Rebel players] are always allowed to ask the Imperial player to repeat any current or previous rules.
— Campaign Guide: Hidden Information

Things Rebel players aren't supposed to know
Event summary

This section is used for the Imperial player's reference only and contains abreviated versions of event triggers.
— Campaign Guide: Event Summary

Effects not chosen when the Imperial player gets to pick an effect

In some cases, an event will require the Imperial player to choose one of a number of effects, which can be instant or ongoing. When he chooses one, he reads the effect aloud and resolves it, but he does not read or resolve any of the unchosen effects.
— Campaign Guide: Mission Events

Anything in the Campaign Guide not read to them by the Imperial player

Rebel players are not allowed to read any of the information found within this Campaign Guide, but they are always allowed to ask the Imperial player to repeat any current or previous rules.
— Campaign Guide: Hidden Information

In other words, the Rebel players are allowed to listen to what the Imperial player reads from the Campaign Guide, but cannot read the Campaign Guide for themselves (since that would allow them to read something they weren't supposed to know). Note that this clearly says that they can ask the Imperial player about rules that have previously been revealed, so the Imperial player must have been allowed to tell them something.
This seems to have been the rule you were rather hung up on. I agree it's probably bad wording, so I'd like to suggest this rewrite that goes with what I think is the spirit of the rules:
Rebel players are not allowed to directly read any of the information found within this Campaign Guide, but the Imperial player must read aloud any information that they are instructed to reveal from it. Rebel players are always allowed to ask the Imperial player to repeat any current or previous rules.

Your particular situation

If I recall correctly, during the first campaign mission (after the tutorial mission), the mission ends after round 6 if the Rebels haven't yet achieved their goal. The Rebel players were understandably miffed when the mission ended unexpectedly.

Unfortunately, this was something the players should have known. As shown above, the rules says that the Imperial player should read aloud:

The mission briefing
All triggered effects
Rules that include the Rebel Alliance symbol, marking the mission progressing or ending in the Rebels' favor

All three of these are present in Aftermath, the first mission:

Mission Briefing
[...]
◆ The mission ends when all terminals are destroyed [Rebel Alliance symbol], at the end of Round 6, or when all heroes are wounded.

So the Rebels should have been informed of this point because it was in the Mission Briefing, was an effect, and had the symbol indicating that it was for mission progress and should be emphasized to the Rebels (in this case, that the terminals needed to be destroyed). And of course, the players are allowed to ask you to repeat it whenever they want to.

I know, for example, that if an Imperial deployment can be triggered by a Rebel action, such as the opening of a door, the Rebels should not be aware of this.

You are correct that in Aftermath the Rebels should not be made aware of this ahead of time because it was not part of the Mission Briefing or any other previously revealed event. But once the trigger for the event happens (in this case, the door being opened), the entire event text must be read aloud to the Rebels.