It looks like this was a consequence of the Trent Tucker rule, which took effect for the 1990-1 season:
The Official Rules of the National Basketball Association state
NOT UNDER 0.3 must expire on the game clock and shot clock when a ball is thrown inbounds and then hit instantly out-of-bounds. If under 0.3 expires in such a situation, the timer will be instructed to deduct AT LEAST 0.3 from the game clock and shot clock. If, in the judgment of the official, the play took longer than 0.3, he will instruct the timer to deduct more time. If under 0.3 remain on the game clock when this situation occurs, the period is over. If under 0.3 remain on the shot clock when this situation occurs, a shot clock violation is called.
The game clock and shot clock must show at least .3 in order for a player to secure possession of the ball on a rebound or throw-in to attempt a field goal. Instant replay shall be utilized if the basket is successful on this type of play and the game clock runs to 0.0 or the shot clock expires on a made basket and the officials are not reasonably certain that the ball was released prior to the expiration of the shot clock. The only type of field goal which may be scored if the game clock and shot clock are at 0.2 or 0.1 is a “tip-in” or “high lob.”
Emphasis added. Basically since then, instant replay is used to determine whether or not the play actually got off on time. Prior to that, the officials would use their best judgment, which would be partly reliant on the timekeeper's buzzer. But with instant replay, they can review the buzzer and clock as well.
Apparently this took effect in the WNBA (1997) and college (FIBA; 2010) later. And of course this would only happen if the game is being recorded. That's true of all professional games but may only be true of some collegiate games.
The actual answer to the question might be the 2002-3 season, as that is when the NBA adopted instant replay. The Trent Tucker rule dates back to 1990, but reviewing it with instant replay is newer.