Joker is a character study movie, it is loosely based on the super villain Joker from the DC universe, but it is not a typical super-hero movie.
"Joker movie would still work even if DC Comics did not exist", as commented by Kevin Smith.
As you stated, near the end of this movie, it is shown that the Waynes are shot and killed but it does not mean that this Joker played by Joaquin Phoenix is the Joker we expect him to be.
- Given the age difference, this Joker by Joaquin Phoenix cannot be the super villain Joker but we have to admit that it has never been explicitly stated that they are the same person. In theory, this Joker by Joaquin Phoenix could be an inspiration of the super villain Joker, who can be at a younger age at the time.
- There is one way to know for sure how this Joker by Joaquin Phoenix fits in with the DC storyline, and that is via a sequel. But the movie director and Joaquin Phoenix have made it known that this Joker movie is an independent movie and there is no plan for a sequel (I would personally say they will seriously consider a sequel now with its success at the box office)
- Some viewers also speculated with evidence that the whole movie could be all happening in this Joker's head, given his unreliable narrator status.