Archie and Maxie basically talk about how they each fulfilled their goals but were swallowed by something before being transported to the USUM world (Archie was about to be swallowed by the sea, while Maxie was about to fall into deep fissure), and then they discuss how they want to achieve their goals in the USUM world as well. After you beat both of them, you then run into two Team RR grunts near the entrance, and then Guzma arrives to stop them. It is during that scene that Archie and Maxie arrive at the room and notice each other. They are about to battle each other, but then they get transported back to their worlds. That's all there really was to them, but the way the two described their goals before you fought them made each of them appear more like their ORAS counterparts (a.k.a. Maxie wanted to expand the land for the sake of humankind to give them more land, while Archie wanted to expand the sea for the sake of the aquatic Pokemon). Other than that, nothing really special about the two.
Lysandre's was nothing too special either. He talks about how he successfully killed everyone in his world, except for Team Flare, with the Ultimate Weapon so that there wouldn't be anymore "conflict or theft" that prevented the world from being beautiful. What follows next is a very similar scene from the XY games where you had to choose between the blue and red button, and the button you chose would determine whether or not the Ultimate Weapon would be activated (although the choice didn't matter anyway, since the Ultimate Weapon was still activated afterward). He comments how you being a "chosen one" has the potential to change the future similar to how he acknowledged Ash as one in the anime. Like the XY games, the choose of which button you choose doesn't matter, though instead of the Weapon activating, Lysandre fights you anyway to "buy time for the weapon to activate." After the battle, Lysandre ponders what would've happened if he had "a trainer like you" in his world lead to him a different choice, but he throws that aside anyway as he concludes his own path is the right to achieve his goals. Then he teleports back to his own world. Yet another villainous team leader who didn't really leave an impression in Rainbow Rocket.
Cyrus, on the other hand, was my favorite of the three, and probably tied with Ghetsis's scene during the RR episode. With Cyrus's scene, he first asks you if the world you're in is the "new world." After you answer either choice, he comments how you have strong spirit because of your desire to protect "something." He realizes that the world he's in is not the he wanted, and then he talks about how he succeeded in creating a new universe in his dimension, but then Giratina (which he refers to as a shadow) swallowed him, and then he ended up in the USUM world. Afterwards, Cyrus notices your Rotomdex and comments, "Interesting... in this world, even the Pokedex is..." He goes silent for a minute, and then he figures you have a spirit, and then he proclaims how we will wipe out emotion and spirit from the USUM world the same way he did in his world.
After the battle, Cyrus wonders, "How are you able to turn those bonds to strength." The Rotomdex tells him that you are kind to all Pokemon. Cyrus goes silent again. He then assures Rotom he won't do anything to the USUM world and will instead return to his newly created universe. After giving you the key to travel to the next area, he ponders, "Had I met you sooner... would things have been different for me...?" This is a contrast from Lysandre, who also pondered the same thing but then shoved it aside and still held onto his belief his way to achieve his goals was the best way.
I think Cyrus's stands out from the other four because he actually gets some nice characterization that delves more into his character. In the DPP games, it is mentioned that Cyrus was a huge technology lover when he was a child, and growing up, gadgets was the main thing he surrounded himself, to the point that he felt more attached to them than other people. Here, we are shown how Cyrus was a technology lover in his youth. Judging by how he temporarily goes silent after seeing the Rotomdex before you fight him, then becoming silent again when the Rotomdex gives an answer, and then saying how he won't recreate the world afterward, you can tell Cyrus seeing the Rotomdex made him nostalgic of those childhood years when he was a technology-lover. After all, it was in technology during those years he found solace and comfort (because growing up, he was isolated as a child due to his parents putting high academic standards on him). The way he also recognizes Rotom also suggests he might have encountered the Pokemon in his youth and had fond memories of it (which is a bit odd since it was Charon that discovered Rotom during his childhood and played with it, but the way how Cyrus behaves around Rotom in USUM could imply he too met Rotom back then).
