The high school (NFHS) and ASA rules are pretty much identical for this play. If, in the umpire's judgment, the interference prevented a double play, then both runners can be called out.
While the actual rule is the same, the variable is going to be what the umpire saw and how he judged it. The double play isn't automatic- there has to be some reasonable chance of two outs having been earned without the interference.
On the initial call, if that's what the umpire judged happened, then he made the right call. But it is kind of odd that a few innings later he would tell you, essentially, that "my judgment was bad on that call and this is what it should have been".
You would probably have to see the play yourself to decide what you would call. Most of the time, the play you describe is only going to result in one out (on the runner who interfered).
To call two outs on this play, you have to assume that the fielder will cleanly field the ball, make the throw to second, have the shortstop handle the throw, make the tag, pivot, throw, then complete the play at first. A lot of assumptions there! Everything would have to go perfectly for the defense and the batter-runner would have to be kind of slow getting to first. It is within the umpire's right to judge that all of that would have happened perfectly, but in reality it might not be the most realistic judgment to make.
The "automatic double play" call is usually reserved for plays where the double play is more imminent and likely. For example, when the force out at second has already been made and the runner going into second interferes with the fielder or the throw to first. On those, the double play is much more likely to be turned- half of it has already been made!- and calling the batter-runner out requires many fewer assumptions.
The other play where this rule comes in is when a runner interfers with a fielder trying to catch a batted fly ball. The runner is out for the interference and the batter is out because a likely catch would have been made.