Out on a home run?

[mastdk96]

Here's the situation R1 on first 2 outs. Batter hits the ball out of the park. As the runners trot around bases R1 gets half way to home plate and walks toward dug out but doesn't enter. Batter-runner trots to home and touches home before R1.
Question here is: Is one of them out? As an umpire do you call anything or wait till the opposing coach appeals? And what do you do if less than 2 outs?

This is for a high school co-ed league that uses ASA rules with a few of their own mixed inbut am looking for the ASA ruling.