Out-of-universe; Although the soundtracks were different in the original versions of the game (Japanese and US), there is something to be taken with the US soundtrack. The Past tracks, which are shared, represent what was originally going to be in every version of the game. The Present represents what changed through No Export for You-esque circumstances, and the Futures represent that the changes were persistent and will evolve, as the Sonic Gems Collection shows. (Not implying that Gems changed the music. Just noting that it has a version of Sonic CD on it. And it was released after Sonic CD, therefore, the future.)—Akamia
Better than that. It also hints that somewhere along the way, there was a Split Timeline event, which after the Past, changed the music for the Present and Future.
The Japanese boss theme samples "Work That Sucker To Death". In Quartz Quadrant, you defeat Eggman's conveyor belt contraption by running the belt until the console platform Eggman is standing on wears thin and he's forced to flee. In other words, you literally work that sucker to death.
In regards to the music, both Ogata and Nilsen were in the right mindset for the musical theming of the zones.
Palmtree Panic's tropical feel: In Japan, the closest to the tropics that Japan can get is Okinawa, which explains why in America the music now sounds like it's from the Caribbean.
Collision Chaos: Both have an urban feel to them but implemented differently. Japan does it like it's Akihabara, while America does it like it's either Chicago or New York.
Tidal Tempest's watery feel to it is implemented a bit differently in both regions. In Japan it has the ocean waves and a ancient feel to it while America uses the ancient feel for the Bad Future, but it still has the watery feel to it with the slap bass sounding like drops of water.
Quartz Quadrant has a sort of rocky feel to it. This is apparent in the Japanese version, while America took rock as rock and roll.
Wacky Workbench has an industrial feel. In Japan, this is heavily reflected in the bad future with the warning siren going off, while America has it sound like a building is being put up.
Stardust Speedway is a bit interesting as Japan does it like a bright night on the road, while America has it sound like Sonic is on a racetrack, and adds a bit of foreshadowing to his eventual race with Metal Sonic.
Metal Madness both involve a techno/rock feel to them. In Japan, it includes the late Casey Rankin chewing out Eggman in rap form that all of his plans have failed and his ultimate weapon has fallen. America meanwhile is heavy on the techno in the Present and Good Future, while heavy on the rock in the Bad Future, showing that Eggman is starting to descend into insanity.
There is a reason for Eggman's robots in this game are all bugs. Unlike in previous games, where the good doctor had avian, reptilian, amphibious, and mammalian Badniks, as the game deals with time travel, having a monkey Badnik in the age of the dinosaurs would cause some cases of Fish out of Temporal Water. Bugs meanwhile were before most chordate animals and are still alive today.
Further Brilliance: Why are the Badniks in CD using living cores that sprout into flowers when shattered? Simple: Plant seeds can remain bioelectrically viable for far longer than animals, so Eggman used flower seeds as the bioelectrical cores of any badniks he would be deploying for the extended time periods from Past to Future. They're also easier to harvest than animals, even if the resulting badniks turn out less powerful/intelligent than the traditional animal-powered ones he can field many more of them at once, and store them for long-term deployments without needing to constantly replace the 'cores' of the badniks due to the small animals dying from old age.
Each Round's Present version gets increasingly industrialized and urbanized as you go through the game. Sonic starts in complete wilderness; the next three Rounds are a mix of urban and rural (outskirts casino, ancient ruins, mining facility), and the last three Rounds are completely man-made in setting (factory, city, robot fortress). Perhaps this is a subtle sign that conservationalism was already losing out on the Little Planet before Sonic even got there, and it took Dr. Eggman's presence as a warning for what might happen.