Is a baserunner automatically out if he runs out of the baseline?

When I was in Little League, I had a call made similar to this one. I was trying to complete a double play on my select team, and as I was tagging the runner who was going to second, he ran out of the baseline and didn't get called out; as a result, I narrowly missed the out at first base, too. It was a terrible call, and I'd suggest making note of this rule in particular to the umpires.