Where to start, where to start...
Apparently, the plate umpire lost track of the count. It happens. It's happened to me before. Anyone that has umpired an appreciable number of games and tells you that they have never lost the count is either lying, or isn't really an umpire.
But just because the plate umpire lost the count, it doesn't change the playing rules. If this was only strike two, then it is strike two, even if the umpire "rang up" the batter. The batter isn't out. The ball isn't automatically dead. Runners may try to advance and fielders may try to put them out.
Base umpire should not have killed the play. We have a live ball, a runner trying to advance and the defense actively making a play on her. No playing rule calls for the ball to become dead in this situation. Let it play out to it's natural conclusion and we'll see what happens.
By the way, for all intents and purposes there is no difference between calling "time" or "dead ball". They are really the same thing and have the same effect. We are taught to use "dead ball" when there is a playing action that by rule causes the ball to become dead (interference, hit batter, ball thrown out of play). "Time" is normally used when the umpire wants to suspend play on his own, not because a playing rule requires it (to sweep the plate, inspect the ball, take line-up changes, grant a coach's conference with his pitcher).
After the play is finished, now either umpire might call time to straighten things out. First, we need to get the batter back at the plate to finish her at-bat.
Next, we need to determine if the umpire's call of strike three caused either team to be in jeopardy. This could play out a lot of different ways, depending on how the play turned. Unfortunately, we'll never know how this play turned out because the umpire stopped it! The only option then is to put the runner back on second base where she started out.
But if the play was allowed to finish, we might have a runner who advanced or a runner who was put out. If the umpires determine that the strike three call put either team in jeopady, then they can place runners on appropriate bases, retract outs or whatever remedy they see fit to correct the mistake that they made. There is no set in stone, one-size-fits-all solution. The rules give the umpires the authority to fix this any way they see fit. What they pick should be the solution that best represents what the outcome of the play would have been had they not called strike three when it was strike two.
Suppose the runner advances to third. Could you say that the defense left the field due to the umpires third strike call? Maybe. As the umpire, that's for you to decide and you could put the runner back on second base.
What if the runner got tagged out? Well, if the runner was trying to advance, then she must not have thought that there were three outs! The umpires could let that out stand.
Or, the umpires could say that both teams had a duty to know the count and game situation and let the play stand, whatever the outcome.
Either option you chose is probably going to tick somebody off, so get ready to handle an angry coach- or two. And do a better job of keeping track of the count!