I haven't actually test this but logic dictates there's really only one answer possible. The logic you refer to is actually called intuition, which is not the same */Spock mode*
Regardless of how many tiles you have available, your city radius doesn't grow again until your city hits size 18. Every worker adds something to the total amount of resources collected, so under all circumstances your citizens collect 1/12th of all available resources in the second ring, regardless of how many tiles are available.
Gameplay-wise this makes sense: you're workers *always* collect 1/12th of the resources, regardless of circumstances. Of course, it's not very intuitive as the absolute number of resources can be much lower even though the people collecting the resources are the same. Think of it this way: the same number of people has to work on much less land, so the overcrowding makes it much harder to grow anything efficiently (small vegetable gardens are far less productive than large-scale industrial farms).
Note that in such cases Specialists become a far more attractive option, as 12/12 * (multipliers) * 3 * 10 food isn't an awful lot compared to 30 * 12 (assuming specialists collect 30 food, this differs per mod)