Yeah, I doubt anyone lost their job over that. If you make a mistake that puts someone's health and well-being at risk - like the pyrotechnician who accidentally set off Taker's pyro too early and burned him as a result at Elimination Chamber 2010 - I could see you losing your job. Jericho said that guy was fired before Taker even walked back behind the curtain after the match was over. But a simple mistake like this won't cost anyone their job. There's been a couple of times in the past when the sound guys hit the wrong person's music (I remember in 2001 during the Invasion when Spike Dudley was coming to the ring and they set off someone else's theme, and then again in 2005 hit Charlie Haas' music instead of Muhammad Hassan's theme right after Hassan got done giving a serious promo (which, if you saw it, was the definition of awkward)) but I'm doubtful anyone was fired over little mistakes like that, or what happened on Raw in the last segment.
Only way I could see someone being let go over it is if they were a brand new person on the job and made a mistake right away, but I doubt even that would get them kicked to the unemployment line.