Let's take this further - hoping this makes it clearer, not muddier.
R1 on 2nd, R2 on 1st. Deep fly to right is caught. R1 did not return all the way to 2nd before advancing to 3rd. R2 tagged up at 1st legally and went to 2nd - the ball is thrown hom and R2 advances to third. Both runners are now on third.
Fielder tags R1, then R2... what do you have?
I think it's safe to say that absent something verbal, they are making these tags because there are two people on base. R1 is there legally... so R2 is out. They can STILL appeal R1 leaving early.
Add in something different... coach yelling "Bobby - #14 left early, throw it to third", whereupon they tage R1 then R2... R1 is out for leaving early. R2 is now NOT out at third, because at the moment he's tagged, he's legally on 3rd base.
That help? Or did I make it worse?