Because this question is not about the actual play, but instead the call and response to it, there's just nothing in the rule book to help. There may be some umpiring documents that would be relevant, but I have no access to them.
So instead I'll give a rationalization based on the principle of "what would probably have happened if the screwup didn't occur" (similar to how fan interference is dealt with).
The proper initial call would have been that the outfielder did not complete the catch, and that the ball is live. The runner on third was not tagging up and would have easily trotted home. An argument could be made that the runner on second could have scored as well, but the conservative arrangement is to give all runners one base. The actions of any player after the out was signaled are irrelevant. The runner on third only went back because of the incorrect "out" signal.
An MLB article by Gregor Chisholm mentions that because this was a replay overturn, the specifics of what to do with the runners were handled by the replay officials, not the on-field crew.
"We go and tell Toronto's manager, [John] Gibbons, that if they overturn this, there would be a placement of runners in New York. We don't place the runners, replay handled all that." -- Third base umpire Jerry Layne
The replay crew in New York then had to determine where those runners would have ended up if the correct call on the field had been made. As a result, it was based on their judgment that all runners would move up one bag and Moncada would be awarded first base with a single.