Every time some new film, employing some new technique or technology, makes an extra large amount of money (or at least gets a lot of hyper attention), the following year sees a relative explosion of films trying to capitalize on what they THINK the new craze is.
CGI was really a subset or a side issue for the film makers. It allowed them to make more films with lots of damage being done, for a lot less cost, but the reason why they used it to do exactly that, was because some big damage-filled movies made a lot of money.
I think what the OP means is action or sci fi or fantasy films with heavy use of CGI. And not just to enhance scenes, which was done pretty early, but where CGI actually substitutes almost completely for using models or stuntmen.
In other words, when Spiderman is dodging between falling buildings while being chased by Megatron, that scene is 99% CGI, and that kind of moviemaking didn’t really get started until Independence Day in 1996.
Looking back at Cinefex covers, the magazine for visual effects fans, the 90s had Starship Troopers and Godzilla that both used extensive CGI for their destructive action scenes. Whereas Independence Day and True Lies were still using models and practical pyrotechnics. Then after them came The Matrix, the Star Wars prequels, and Lord of the Rings, which ushered in a new era of extensive CGI for synthetic people and environments.
That is one interpretation but I still don’t think the question is clear. I think he is asking about a style shift that emphasizes ridiculous explosions and really fast camera cutaways. That is the signature of a Michael Bay style of movie-making and I do not approve. I have tried to watch those styles of movies but inevitably just fell asleep just because it seemed epilepsy was setting in even though I don’t have it myself. Fast cuts just bore the shit out of me. I very literally fell asleep during Spiderman II in the theater because of sensory overload and haven’t watched a superhero movie since and have no intention to.
I think that is what the OP is talking about but it has more to do with editing than pure CGI. People like me don’t need every movie to be like Out of Africa or even Casablanca. All you have to do is not actively irritate the viewers with cinematic gimmicks (I am looking at you Blair Witch Project). If I never see another shaky cam or an unrealistic explosion in my life, it will be too soon.
The original Charlie’s Angels movie was really good at parodying that style before it became a constant theme. Before that, there was the Arnold Schwarzenegger Commando that was absolutely beautiful in its earnest absurdity.
Picking 2015 as a year surely deep within the “violent cgi pyrotechnic” age, I count 10 films in the Wikipedia list that are closest to being likely to meet OP’s criteria, out of 329 films listed (plus or minus a couple, my counting may not have been perfect.) That is 3 percent of the films listed. 8 of those fall within the blockbuster season of March through July (I’m making an executive decision to place “FANT 4 STIC”, released August 4th, in that block.) leaving only 2 for the rest of the year, such as Oscar season and the dump months. So it is very serious confirmation bias to get the impression that 75% of new movies fit that criteria. (Though those movies do get a large percentage of the press and the box office returns.)
I think the difference there is that the film was ABOUT a singular building fire. The sort of films you’re talking about with Independence Day or 2012 or San Andreas or The Avengers have buildings getting knocked down or blown up just as a matter of course. The story of a skyscraper and the people within it in those movies is irrelevant – it’s just another thing to get 'sploded.
1991 James Cameron directs Terminator 2: Judgement Day. Already known for action films like Terminator, Aliens and The Abyss, he makes use of groundbreaking CGI technology first used in The Abyss to create the “liquid metal” effect of the T1000.
1994 Roland Emmerich directs Stargate, his first film to crack the $100 million mark. Mostly practical effects, but with some use of CGI for the alien’s head pieces and the Stargate’s event horizon.
1995 Michael Bay directs Bad Boys starring Will Smith and Martin Lawrence. It is the first of a series of films including The Rock, Armageddon, Pearl Harbor, Bad Boys II, The Island and Transformers 1 through 7 that share his trademark style - kinetic action scenes, loud music, people staring at American flags while planes fly overhead and lots of explosions.
1996 Roland Emmerich directs Independence Day, cementing his place in history as the father of the big-budget CGI disaster movie. He will follow up with several more films including 2012, The Day After Tomorrow, and Independence Day 2 (and the upcoming 3).
So the specific answer IMHO is the violent CGI pyrotechnic film craze started around 1995, 1996 with the films mentioned above. While there have always been violent action films, and decent CGI has been used in film since the late 80s, it was in the mid 90s where the technology had reached a point where it could be added to films on a scale and level of realism that enabled big budget action directors like Bay, Cameron and Emmerich to create the loud, crazy pyrotechnic explosion-fests they always dreamed of.