In ASA, the runner may return to the white without liability to be put out, assuming she did not make an attempt at 2nd.
POE 31 says If the batter-runner overruns first base and returns to the colored portion (rather than the white), sufficient time to touch the white should be given, particularly in youth play.
If the fielder tagged the runner right away, I've got a nothing.
I don't know what "sufficient time" means except that it is an umpire judgment call.
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