FWIW, there is no fake tag during a dead ball.
Taking @834k3r's statement a bit further, there is always a big element of HTBT on these plays. Sometimes though, the optics can change what has to be done.
One of the worst collisions I ever had was the result of the catcher moving up the line for the tag (legal), a "country big boy" runner bracing (legal), and the catcher tripping (legal). It wasn't going to be pretty, but the trip propelled the catcher and took away his ability to check up. I did end up ejecting the runner, because he hopped up and flexed over the catcher. Of course, I spoke with the coach at the moment, but what was more interesting was the player coming to talk to me afterwards.
I explained to him that I knew he was bracing and checking up, and I knew the catcher tripped. I knew it was not malicious or intentional, even though it looked bad. I told him I already knew I wasn't going to toss anybody after the collision. The problem was the taunting afterwards which altered the optics of the whole thing . . . he totally understood I had to at that point.
Back to the OP . . . so what are you calling a "fake tag". Was it light horseplay? Or was it rougher and something that understandably offended (I'm not saying was justified)? I'm not excusing the runner in any way. I'm trying to figure out if the fielder needed to go, too, or if it was a "did you learn your lesson not to do that for this exact reason?".
One issue we have at the amateur level is we do not know the history between teams or players. Did these guys have a history? Once had an incident that resulted in an ejected coach and a forfeited game (refused to leave, no ACs). Afterwards a parent approached us and the site director "in the parking lot dressing room" to tell us, "Oh yeah, we played them last week (3 states over) and the cops had to be called." Damn, I wish we had HURs.