OK, the call is "
PU directs batter home, and she runs home (touching it again)."
Presumably R1, not the batter.
The rule says "play stops" at the pitcher control demo point, at which time the Umpire artificially places the runner(s).
By that, R1 obviously past halfway when "play stops" and when time is called, looks like a correct call.
The conundrum is what "play stops" is intended to mean.
This paragraph is probably irrelevant to the call unless 3rd base dying down is needed.
"
During this time, coaches are yelling for R1 to return, but she does not hear anyone until JUST a bit after PU calls time, at which she begins returning to third (skipping home, but that never comes up). Everyone's yelling at this point, PU holding his hands up, calling time progressively louder. Runner makes it back to third right as it dies down."
disclaimer: this is another local rule.