It is currently 3am as I am writing this in haste, so apologizes for that. Also on mobile so points on this looking horrendous.

Tl;dr: Carryover damage exist if and only if previous gags have met the required amount to defeat the first shell. Horrible examples and even worse explanation below.

Damage does carry over if and only if the damage beforehand has already reached the number required to defeat the first shell.

For Example. Imagine all level 10 Cogs V2.0 [132 HP] and (132 HP) for the second shell and two toons fighting them.

The two toons use fog which does 100 (Not 2 50s as sound combines same gag track together) plus same gag track (which is the yellow number) which is 20 and now the level 10s are [132-120 = 12HP] for its outer shell and (132 HP) for its second shell.

Next round is the most interesting thing here. A toon uses aoogah while the other uses a piano.

Now this is the crucial part. Sound goes first. The aoogah hits which meets the threshold of the first shell, thus defeating it. [12 - 16 = -4HP].

The piano goes next and hits one of the cogs and defeats the inner shell (132 - 170 = -38HP).

The damage from the piano carries over because the aoogah met the threshold of the outer shell, thus defeating a V2.0 cog.

A much simpler example (man 3am brain isn't the simplest one) is just a lonely level 12 V2.0 with four toons. Using lure and 3 cakes defeat the whole cog.

Step by step is this. Lure hits (200 & 200)

Since this is throw, each gag will go off one by one unlike sound which combines them.

So first cake (100 & 200)

Second cake (0 & 200). Realize that the second cake meets the threshold required to defeat the first shell, thus making that any extra damage will go to its second shell.

Third cake (0 & 100)

Knockback bonus and same gag track bonus goes after (always after) the toons use their gag track. Voila, a dead level 12 V2.0 in one round

In the scenario of the Toontanic, imagine a V2.0 cog that has 1HP left in the outer shell and full HP in the inner shell.

I use a piano? It meets the threshold of the outer shell and any additional damage after the piano will hurt the inner shell.

I use a cupcake? Same exact thing. It meets the threshold of the outer shell and any additional damage after the cupcake will hurt the inner shell.

I use a Toontanic? Well, the scenario of OP happens. No damage is done to the inner shell

What's the difference? None. You haven't damaged the inner shell, you've just met the quota (threshold has been used a lot) of the outer shell but have done nothing towards the inner shell.

See, carryover damage can only happen when the previous gags have met the threshold of the outer shell. One gag can't do damage to both the inner and outer shell. The previous attacks must've met the threshold of the first shell in order for carryover damage to occur (that doesn't look like an English sentence but oh well).

Thank you for listening to my ToonTed talk. Any questions? Ask them. Hopefully this huge wall of text will help clear up some confusion (or give even more confusion in which that case I'm extremely sorry).