First off, the best move would be to ask why the runner at 3rd was called out? Just going by the scenario presented - he didn't do anything wrong.
As for the runner back at first: If he didn't retouch 2nd on his way to 1st he would be out. That's a simple one.
If he did touch 2nd you need to look at:
5.09(b)(10)
(10) After he has acquired legal possession of a base, he runs the bases in reverse order for the purpose of confusing the defense or making a travesty of the game. The umpire shall immediately call “Time” and declare the runner out
So, was it an attempt to confuse the defense? I guess you had to be there, so - maybe. Was it to make a travesty of the game? No, it was just part of a play.
One other consideration is that if the pitcher had the ball and was ready to pitch you need to look at:
Rule 5.06(a)/5.06(c) Comment: If a runner legally acquires title to a base, and the pitcher assumes his pitching position, the runner may not return to a previously occupied base
That doesn't apply here apparently, but it's one of those things you can point to in order to frame an argument. In other words, he should only be out if he acquired the next base AND the pitcher was ready to pitch. Since both of those conditions were not met, it's just nothing and he wouldn't be out. You can't declare a runner out just for doing something weird, he actually has to have broken a rule. If there isn't a rule preventing an action, it is generally accepted to be legal.
So you are left with - the runner at 3rd should be safe. The runner at first would only be out if the umpires felt he was trying to "confuse the defense" by running backwards. Other than that he should be safe as well.
In the best case scenario, the umpires called the wrong runner out.
I find the officials guilty of improper enforcement and sentence them to a weekend of remedial slideshows.