ZC is a little different than the standard GCT Files you may be used to. These Gecko Codes are packed in with the save data file. There is a portion of the save data that is unused but the entire file gets loaded into RAM. This means by placing the codes in with the save data they will be loaded when the game is started. Because the save data is being edited for these codes a new ROM has been made for use with them so that it doesn't interfere with the standard one.
There are two versions of the new ROM that you can get. One is just the vanilla game while the other has changes such as shortened or removed cutscenes, use of unused spawn points, etc. This speeds up the gameplay allowing for more optimized segment practice.
Because these codes are part of the save data the state of the codes are saved with Song of Time. So, for example, if you have the codes enabled then use Song of Time followed by turning the console off. Then the next time you launch the game with codes they will already be turned on. Additionally the Mem Files are stored in the save data as well. This means that even though hard resets or powering off the console your Mem File will be preserved and usable the next time you play the game.
Make sure to check out the User Manual to learn how to use ZC.
You may notice that there is a Nintendo 64 version available for download. This is strictly just a patch to create the modified ROM which then can be used with an Emulator like Project64 or a Flashcart on the Nintendo 64. The custom Save Data and Gecko Codes are not for Nintendo 64 as they will only work on the Nintendo Wii. This means that Nintendo 64 only has the shortened cutscenes available to it and no codes.