Once a student clicks on the URL to your assignment, they will have to log in. It is very important that they log in using the "Google" red button.
"IT STILL ASKS THEM TO ADD A CLASS CODE"
If that is the case, it's probably because the student enrolled the Google Classroom group and it's still not imported to Edpuzzle. There is an easy solution.
To sync both platforms once a student has joined your Google Classroom group, you just need to follow these steps:
1. Go to www.edpuzzle.com and log into your account.
2. Go to My Classes and select the class where your student should be registered.
3. Click the "Import students" button in the top-right corner
I hope this clarifies all your doubts, otherwise, let me know, I am happy to help you further :)