As for the Avatar trilogy and the Time of Troubles, it was indeed used as a justification for various 2nd edition AD&D rules changes such as the elimination of the assassin class, rather than simply applying such changes retroactively. For example, the Forgotten Realms had a patron deity specifically for assassins named Bhaal, and as part of the Avatar storyline this god was destroyed along with all members of the assassin class, rather than take the option of having all assassins retroactively become thieves or fighters who practiced assassination.
Cyric took over all of Bhaal's duties after Bhaal was killed. Cyric became the god of murder and assassins (and a number of other things).
That being said, a sub-class removal is hardly a change in rules - the entire psionics class was removed from 2nd edition, until the Complete Psionics Handbook was released.
Assassins were then introduced as a class kit in the Thieves' Handbook - and indeed that's really all they ever were, a subclass of Thieves.
Like a lot of things in 2nd edition, they were moved around, to streamline and to sell more books. In the end, you could have your 2nd edition be exactly like 1st edition, if that's what you wanted. If you wanted it official, you could buy the extra books with the extra information.
The Avatar trilogy had nothing to do with rule-changes between 1st and 2nd edition AD&D. It was simply a function of needing to publish the Forgotten Realms for the 2nd edition - not because the original Forgotten Realms setting was in any way incompatible.
In the 2nd edition Gold Box FR setting there was even a leaflet / addendum which explained in one page what you had to keep in mind if you had 1st edition rulebooks and the Gold Box FR setting.