That's the common perception, but to be fair, the Disney Renaissance is from 1984-94. That's when Michael Eisner, Jeffrey Katzenberg, and Frank Wells were running the show. Granted, The Little Mermaid is the film that started the "magic" but things didn't happen over night.
The Great Mouse Detective and Oliver & Company aren't "classics" but they paved the way. They served as a learning experience. Then, there's Roger Rabbit. Most people don't realize how important that film is to the Renaissance. On the surface, Don Bluth was Enemy #1 but it was really Steven Spielberg. He produced the Bluth movies and then came to Disney to show-off. That's the straw that broke the camels backs. The Little Mermaid was essentially an F-you to Spielberg.
In `94, when Frank Wells died and Jeffrey Katzenberg left the company, is when everything changed. The Lion King was really the end of the Renaissance. Michael Eisner didn't know how to run the company alone. That's why the quality in Disney Animation declined. The post-Lion King films have their fans but we can all agree that they can't compete with what came before. Those were the true classics.
It kinda does. Rescuers Down Under, like Mouse Detective and Oliver, is important to the history. They made a lot of animation break-throughs with that movie and it opened the door to Pixar. Nightmare Before Christmas should also be considered. It was released through Touchstone since it was "too dark" but the film is a classic in its own right and continues to be a money-maker for the studio.
I just counted the ones that are often identified with DR and these are the films. You could make an argument, but I don't identify the films with the era. I'll admit its because its probably because of quality because I always found Rescuers Down Under to be boring (The first Rescuers film was so much better). I liked Oliver and Company though.
But to be honest, I'd say it starts with The Little Mermaid because that's the film that jump started Disney's run of going back to their fairy-tale (or fairytale-like) roots, hence the term Disney Renaissance. A wave of quality creative activity happening due to embracing the past.
People say it ended with Tarzan because that was the last film have music interludes. It wasn't a musical, per se, but it did feature a lot of music montages.