I think the Arcane Age and Karsus's Fall entered canon sometime around 1995-1996.
Karsus was described as a "lesser-known" deity in a half-page article by Eric Boyd published in the February 1995 issue (#104) of the Polyhedron magazine. At this point, Karsus is not a dead power and his demise (from greater deity to demigod) was attributed to his poisoning by a Netherese mage named Wulgreth, who sought to steal immortality from Karsus (ironic, isn't it?). So we can conclude that early 1995, Karsus's story as we know it was not yet canon.
TSR released the Netheril: Empire of Magic (N:EoM) boxed set in November 1996. Yet we can argue that Netheril storyline was already entering the FR canon before N:EoM's publication based on evidence from the sourcebook Faiths and Avatars (F&A), which was published in March of that year. F&A has plenty of information about Mystra that foretells the then-upcoming Arcane Age storyline: Mystryl is given as one of Mystra's aliases; her speciality priests can also be of the CN alignment (Mystrl was CN); one of Mystra's symbols is none other than Mystrl's symbol, a single blue-white star. It is worth noting that one of the authors of F&A was Eric Boyd.
Powers and Pantheons (P&P), a companion to and continuation of F&A, was published in 1997. At this point it is clear that the whole Karsus story is canon: P&P lists Karsus as a dead demigod, describing explicitly the events in the earlier Netheril material; including his 12th level spell, and how he used it to steal Mystrl's power and ended up dead.
1998 saw the expansion of the Arcane Age material further with the publication of Cormanthyr: Empire of Elves. This product is also in full support of the Karsus's Fall story, including all the events in the earlier Arcane Age material.
The conclusion is that Karsus's Fall became canon during the 2e of AD&D.
Ao created tablets of new rules intended to restore peace and balance to Toril.
In a video of a 2012 Gencon panel featuring Forgotten Realms novel authors, What is the Sundering (Part 1), it is stated that the supreme overgod Ao intentionally re-created the tablet of rules that separated the worlds of Abeir and Toril, intended to restore balance and order to Toril.
The events of the D&D 4th edition era where the now twin worlds of Abeir and Toril were recombined into one world are revealed to be the result of Ao destroying tablets of rules he created, those that divided the worlds in the first place long ago. Originally, their purpose was to divide the world into Abeir, where the Primoridials held sway, and Toril, where the Gods had power.
However, when two deities stole the tablets and began fighting amongst each other, Ao destroyed them to teach the gods a lesson, and the worlds were recombined. Unfortunately, this only made things worse, and so Ao set about recreating the tablets and dividing Abeir and Toril in two once more, but this time with a new rule limiting the ability of the gods to damage Toril in their petty squabbles.
Ao's reasons are described at 11:35 in the video:
Once it is over, the word of Ao declares: The Era of Upheaval is ended. Great stories remain to be told in this era, but they are not the stories of gods and godlike beings. They are the tales of mortal heroes, taking a stand to preserve the world they love.
This ethos reflects Wizards of the Coast's policy for the focus of Realms products and novels, which we learn at 23:20 in the video is intended to return to "the heart of high fantasy", and at 31:15 it is stated that WotC wants individual characters to be significant actors (e.g. why player characters should have to save the day instead of leaving it to deities).
As such the novels of that era will focus on the actions of people, not the gods or Ao. It may be that no novel or sourcebook explicitly references this lore about Ao stated by Wizards of the Coast. At 36:48 in the video, it is said to be likely that no protagonist of these novels is likely to be fully aware of the situation with the gods, and even Elminster may only partially understand it.
It should be noted that gods can, to some extent, defy Ao. It was gods who stole the tablets from Ao in the first place, and Tiamat has a loophole which allows her to be summoned in person to Toril. This suggests that Ao's new rules are significant, but not necessarily absolute.
Best Answer
According to Netheril: Empire of Magic (N:EoM), at the time of the Netherese there were very few human deities and each one of them carried very many portfolios. It seems like as the millennia went by, those portfolios got shared by many new powers.
For Mystryl, the list went like this: Magic, spells, the weave, wizards, spellcasters, energy, creativity, knowledge, invention, song, time, spring (page 49 of The Winds of Netheril).
We can compare this list with the portfolios given in the FR Adventures (FRA) and Faiths & Avatars (F&A) sourcebooks. We see that every portfolio except Time is covered: Azuth (mages, energy according to FRA; wizards, spellcasters according to F&A), Oghma (knowledge according to FRA; knowledge, invention according to F&A), Lathander (spring according to FRA; spring, creativity according to F&A), Milil (song), and of course Mystra (magic, spells, the weave).
Given that every other one is somehow covered, and the great many commonalities between N:EoM and F&A, I would agree with Carcer's statement and say Time appears to have been intentionally left out by TSR. (F&A lists Julia Martin with Eric Boyd as designers. For N:EoM, Julia Martin is listed under "additional design" and Eric Boyd is listed as a proofreader.)
There is one final curiosity: Amaunator is mentioned (in both N:EoM and F&A) to have misinterpreted some godly contract and wanted to preside over passage of time, but decided not to interfere with Mystryl. It looks like after Mystryl's demise, he still did not claim Time. So perhaps Mystra could still be the "hidden inheritor" of the portfolio and might someday claim it openly. It might also be worth mentioning that three "time gates" that allow characters to travel back to the Netherese period were still active as of 1370DR, and they were being protected by Mystryl's magic (N:EoM). It would be an interesting scenario to have Midnight/Mystra sending an avatar/proxy to meet her old self, Mystryl.
On a related note: Here is a list of powers from F&A who grant major access to the sphere of Time to her/his speciality priests: Amaunator, Auril, Chauntea, Cyric, Eldath, Kelemvor, Leira, Mask, Mielikki, Myrkul, Mystra, Shar, Silvanus, Sune. We broadly see that they are mostly deities of nature, death, or deception. If you really want to assign the portfolio of Time in your own game, consider one of these.
Deities followed by chronomancers
There is an article with the title Chronomancy & the Multiverse, version 1.1 by Roger E. Moore, published as "an updated and expanded excerpt from the Chronomancer", a 2e accessory. The article was made public by the WotC on their free downloads for previous editions site. This article has a section of the effects of chronomancy in the Realms, and relates time with deities of knowledge and writing. It is stated: