We need to get this clarification included in the rulebook. I've seen too many misinformed umpires call runners out for this.
I should note that NCAA has different rules for the look back scenarios. I won't address those difference here since the rule creates enough confusion for the codes (ASA, Federation, PONY, etc) that most are familiar with.
Unfortunately, most rule books place this information in the Points of Emphasis or Rules Supplement and not in the rules themselves. There is, I believe, a good reason for it though. The LBR has its own entire section under "The baserunner is out." The exceptions (when not to call the runner out) are too long to enumerate and aren't listed under "The baserunner is NOT out."
There are also some small difference between ASA and PONY. When the batter-runner is committed to return to 1st base because of her actions after overrunning the base, she must do so non-stop. PONY just says she must return to the base.
Every umpire test/quiz I have helped write over the years has included at least one of these plays.
In 1994, the umpires misinterpreted the rule and misapplied it when the batter-runner rounded 1st base, continued non-stop about 40 feet toward 2nd base, stopped, and immediately continued to 2nd base. The umpires called the runner out. We ended up protesting the game and had Bristol on the phone until it was almost dark because the umpires kept changing the facts to suit their call. Ultimately, the call was overturned.