When do new rounds start in daily tournaments?

According to chess.com help, "the next round of a tournament will start once all the current round's games have been finished". However, this seems inaccurate. I'm playing a tournament in which round 2 has already started even though there is a game in round 1 that hasn't finished. That game is inconsequential: both players are already eliminated regardless of the result. I like that approach, there's no point in delaying the beginning of the next round if all the ongoing games in the current round are inconsequential. But that's not what the rules say. So what are the actual rules?

Yes, I have seen the system work this way.
For example, even though it is clear who advances, if they can reach each other thanks to one of the remaining games, the advancement of the round is delayed until- (even though that does not change who qualifies).
I think the rule could be: "Until each of the qualifying positions is defined", not said, but the one that applies.

That makes sense. I am also participating in another tournament that hasn't advanced to the next round yet, but the only games remaining in the current round are between players who are already qualified. The result of those games will only determine who takes the first position of the group.

So you think that the rule is that tournaments advance to the next round once the qualifying positions are determined. Have you seen a tournament advance to the next round when one of the qualified players still has games ongoing? For example, let's say there's just one game remaining in the current round between a player who has already secured the first position of the group and a player who has already secured the second position. Does the tournament advance to the next round before that game finishes?

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I have two examples of this that have happened to me, which comply with the "Until all qualifying positions are defined."
I'm not sure what type of game you're referring to in the example above. If one between two players who advance to the next round, or between one who advances and another who is eliminated. But I show both cases.

1. Eliminated vs qualified
Although this tournament has not yet advanced to the next round, the players who would technically advance are already shaded. https://www.chess.com/tournament/sdcvbnhmsadf/pairings

Everyone practically does not move from their position and these games do not prevent other groups from advancing to the next round once they have been decided.

2. Qualified vs qualified

This tournament has been over for a while, but I choose it because it is much more difficult to find current cases.

That would be what was at the time the remaining game (me with black pieces), and according to how the table looked all positions were assured.

Then once I finished my game against the third place where I secured the pass the next round continued.
Some round 4 games ended and later that game of mine with black pieces ends.

https://www.chess.com/tournament/fighters-2/games

(Ignore the dates a little, I am not agile in correspondence)

Thank you for your detailed answer.

Your second example is just what I was thinking about: the only remaining game is between a player who has already qualified in first position (Makaki) and a player who has already qualified in second position (you). That's crazy, by the way. You were playing the third and the fourth rounds of the same tournament at the same time!

Your first case is also interesting, and I hadn't thought about that: what happens when the only remaining game is between a player who has already qualified and secured his qualifying position and a player who has already been eliminated? I guess it must be the same as in your second example: probably the tournament advances to the next round even before that game is finished. But the example you have chosen doesn't illustrate that. In that tournament there are many games in the current round that haven't finished yet, and several of those games are going to determine who qualifies for the next round, so that case is not so clear.

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