Are you sure its not the "conditional moves" feature for online games?
It's a feature that allows you "premove" your moves upon a "conditional" move your opponent makes, you can set several conditional premoves if you are a paying member, non-paying members I believe only get 1. So if your opponent deduces your next move correctly, the computer will automatically play their "premove" in correspondence to your move.
Though double check with your opponent.
Some time ago, I experienced a few players (online play, not live) who responded to my moves in a near-immediate manner, yet were not online. Recently, I experienced this again.
Each time, I see that my opponent has dozens of active games, all apparently waiting for their opponent to move -- hence the rapidity of play is not limited to my game.
After one simple Google search, it became clear there are potentially several automated "bots" that one can download and use -- some brag about managing up to 100 simultaneous games.
As a paying member, I find this deplorable that the Chess.com tech/IT team is not able to close holes that allow for non-human scripts to make moves in online games. It's not hard.
Has anyone else experienced rapid-response play in online chess from opponents who aren't tagged as being online at the time of their move?