The map is available in any game mode, you don't need to start it as a Franchise zoo and you don't need to do anything special like "click the globe" or whatever. After you click "New Zoo" from the main menu, You just have to select "Tropical" for biome and "South America" for continent, and then just to the right of that change the "Terrain Type" to the Sculpted option.
If you do all that, you'll get that special map, regardless of what game mode you chose.
You might need to own the South America DLC though. Not sure if that "special map" is available without the DLC. I know the sculpted map for Oceania-Desert is a unique one too, but only if you own the Australia DLC.
There is a unique sculpted map for each biome, and then in addition to the 6 biome sculpted maps, there are two special ones. This one, for Tropical-South America, and the other one I mentioned for Desert-Oceania.
If you Google search for this you'll see all kinds of silly hocus pocus theories on how to get the "special map". But all of those discussions are old, from before they added the toggle option that let you pick a terrain type when making a new zoo. It's now easy to get the special maps and you don't need to use any hocus pocus.