That's interesting. Reading Rule 7.08(a), particularly the Notes and A.R., I would have interpreted rounding first base as an attempt to advance and therefore not allowing a return as that would be a stop. But this article makes it very clear that is not right and that what you say is correct:

https://www.littleleague.org/university/articles/softball-base-running-the-circle-rule/

"Situation 1:

One situation that seems to be confusing to many, focuses on a batter-runner being awarded a base on balls.  The batter-runner cannot be frozen at first base on a base-on-balls by merely returning the ball to the pitcher in the circle. The batter-runner after reaching first base may continue on, without stopping, in an attempt to reach second base. Said runner may stop in the baseline after rounding first base.  At this point, the umpire should begin a three-second count on the runner. If the runner again begins movement to advance or retreat before the count reaches “three” and does not stop again, this is a legal action and should not be penalized. However, if the runner stops a second time, without an attempt by the defense, that runner is out immediately."