That's because the remake merely just doubles the ring count for each subsequent rings UFO that is destroyed. In the original, it uses a separate counter for the chain bonus, which is initialized as 20, and doubles for each subsequent rings UFO, which is then added to the ring counter. Here is a demonstration.
I'm placing my bets on the original, to be honest, with how messy the code can get. Bonus quirk: there is a bug where a Tamabboh's missiles will despawn if it flies past a block with solidity. This is due to an oversight where it checks for floor collision (aka, it checks for collision with a block downwards) even if it's moving upwards. When it moves high enough past a block with solidity for the downwards check to register as touching the floor, it despawns. The first bit just checks if the missile is on screen, and if not, despawn it. Then comes the floor collision check without an additional check to see if it's moving downwards. Here is a visualization of this. Notice how the left missile despawns once the bottom of its collision sensor touches the block with solidity.
If you have an astute eye, you can see that the drowning countdown numbers are actually bubbles that come out of Sonic's mouth. (Yes this is in all the Genesis titles, but it's also in CD, so...) Also, the colors are a bit messed up here in Sonic CD for when the number forms. The reason for this is because they are using the wrong palette line. The number itself uses line 1 for the yellows, but it seems they got a bit lazy and also made the bubble formation use it as well, when they were designed for line 0, using Sonic's blues. The reason why this is because in prototypes, the fully formed number graphic weren't yellow like in Sonic 1, but rather also appeared like a bubble, so it used line 0. When the numbers went back to being yellow, they went back to line 1, but took the formation with it. The code changes between v0.51 and the final are highlighted here. When the number gets spawned, its palette line is set from the start, and also changed the initialization code to OR the tile ID instead of directly setting it so that the palette line change can go into effect. Interesting thing to note is that these graphics appear to stem from a later prototype of Sonic 1. The numbers originally being bubbles makes the whole thing with them coming out of Sonic's mouth make more sense. The 2011 remake mostly fixes this, but the lightest shade of blue was accidentally left as the regular one instead of the underwater one, so it appears more purple instead of baby blue.
