Serena at U.S. Open Final 2018
After reading the article I'd like you to also find the video of the exchange and see that no matter what else happened it is clear that once Serena lost her focus on play that she had no chance of winning. Naomi played superbly and it is very likely that she would have won anyway and that part of the issue was that Serena extends her unhappiness with losing to her behavior that often goes against the rules of tennis behavior in tournaments.
The Chair Rules
The question of her coach giving signals in the stands is hard to define as an infraction and I really wonder if it shouldn't be done away with altogether. I don't know from what I saw if the umpire made the right call on that or not.
From there though, racket abuse is clearly an infraction and once the first warning was given Serena had to know it might cost her a point which it did. That really set her off and rather than bearing down and going for a win she turned her ire toward the umpire which in my opinion was not only regrettable but cost her dearly. In modern sports and especially tennis there is nothing to gain from arguing and in this case abusing the chair umpire. He kept cool up there and after one harangue after another aimed at him he took a game from her and he is probably safe for having done it.
Keep Your Cool
This match and the outcome is a clear example why learning to tame your emotions in a match and focusing on the task at hand is more important than acting out against perceived injustices. You have to realize that if an umpire is doing things against you that probably you can do nothing positive about it by raising a big fuss. It won't help you win unless somehow it distracts your opponent and then by actions you are using gamesmanship, something Nastase was a master of doing to help break down an opponent's concentration. He among others back in the annals of tennis history in the 70's is why these new rules for behavior are in place. We ended up here because of poor behavior from the past. It took away from the sport where tennis became secondary and the antics became what you remembered. So it was at the 2018 women's U.S. Open final.
Other players this year have acted out and have paid with lost points, games, matches, and fines. In the end you'll notice that the happiest and most successful players are the ones with fewer battles with officials.