End of combat / turn order dilemma

To keep things simple:

In a party of adventureres, there are 2 rogue’s, we’ll say one has an initiative of 20, the other of 10.

The rogue with the initiative of 20, kills the second-to-last enemy minion, and doesn’t use their movement as they are offering flank advantage to another member of the party.

The 10-initiative Rogue’s round in combat, they kill the final enemy minion, and then use their movement once “combat had ended” to rush to the boss and loot before anyone else had the chance to.

The DM allowed this as it was “part of their turn to move”. But if all of these actions are happening within the same “6 second time frame” that “Rounds” work with, the Rogue’s would have killed their target’s at the same time, both would have noticed that combat was over, and both could have made a rush to the boss loot.

I was not either Rogue in this situation, but from watching from the side, I feel like the 20-Rogue got put-down for having a better initiative. Looking for thoughts / rulings on how this should have went down.