This episode contains examples of the following tropes:
Arch-Enemies: As with the games, Team Magma and Team Aqua are this; while they're both extremist organizations who Would Hurt a Child (or anyone else that they need to in order to get their way), they have fundamentally opposite goals from each other: Team Magma thinks that the Earth should be made entirely of land and wants to eliminate the oceans, while Team Aqua thinks the whole planet should be sea and wants to get rid of land masses.
As You Know: The leaders of the Magma and Aqua teams refer to each other by name and state the guiding beliefs of their organizations out loud, despite the fact that they both know what both Teams stand for. It's for the benefit of both the out-of-universe audience and the two separate in-universe groups of eavesdroppers (the twerps and Team Rocket).
Call-Back: Ash and May recognize Team Magma's uniforms from when some of their members captured them in "A Ruin with a View". Since this was at the very beginning of the arc before Max and Brock joined up with them, the two of them are unfamiliar with the group.
Early-Installment Weirdness: The leaders of the Magma and Aqua task forces are based on their designs from the original Ruby & Sapphire games, but for some reason, in the dub, their names are given as Harlan and Isabelle, respectively. In all subsequent appearances for both teams, these characters are instead called Tabitha and Shelly, matching their names from the games.
Even Evil Has Standards: Despite their animosity, both Team Magma and Team Aqua decide to avoid any unnecessary battle when it turns out the cave they raided isn't the Cave of Origin they were looking out for, deciding to leave peacefully without engaging the opposite organization into a brawl.
Never Trust a Title: The title of the episode seems to suggest that the three titular teams (Team Magma, Team Aqua, and Team Rocket) will be coming up with some sort of scheme all together. In the actual episode, the three of them are all on different sides with their own plans; Teams Magma and Aqua are established to be Arch-Enemies with opposite agendas, and Team Rocket's schemes are their usual small-time level, unrelated to either except for being in the wrong place at the right time.
The heroes don't get into any kind of skirmish with the members of Teams Magma and Aqua this time, and in fact spy on them from above without either group ever learning they're there. Ditto for Team Rocket; their fight with the twerps only occurs after the task forces from Magma and Aqua have left the vicinity.
This goes for Magma and Aqua vs each other as well; the leaders of their two groups exchange passive-aggressive dialogue and clearly consider battling each other, but ultimately decide not to once they learn that whatever they're both looking for isn't there, and leave without any violence.
