This show, like just about all of the DC shows, are their own continuity. To say that the New 52 made watchers question what was going on is wrong. Not watching the show or lack of knowledge of the characters would do that. The creators even said this is a different Earth from the continuity pre and post 52. There are at least 20 things I can name that let you know this is no set comic book continuity. This show is it's own continuity but that's what made it great. Artemis' mother being Huntress, Kal'dur being Aqualad, Rocket being a member of the Justice League after being a member of the team, no Donna Troy, Arsenal and Red Arrow being 2 "different" people. They basically did whatever they wanted for the show and that made it pretty close to the level of quality of the Justice League.
The New 52 didn't kill this show. What did it is embarrasing to say and really needs no explanation. Money.