If runner had crossed the plate before the out was made at third then the run should have counted.
SECTION 61 of NFHS Softball Rule Book:
A timing play is a play when the last out of an inning is not the result of a force out and the exact time of the out may or may not allow a run to score. If a runner should touch home base an instant before the last out (which is not a force out) is made, then the run would be scored. If a runner should touch home base an instant after the last out then no run would be scored.