The -j (junk paths) flag you set is killing what you want since it strips out the folder paths. That being said, however, I don't really see a way to just do second+.
From the Man Page:
You may want to make a zip archive that contains the files in foo,
without recording the directory name, foo. You can use the -j option
to leave off the paths, as in:
zip -j foo foo/*
From what I can tell, that is just how it works in "zip" (nothing in the man suggests otherwise).
Edit: I was a bit after the other guy as I was trying to find out how to do what you want.
Why don't you just navigate to the directory and zip it? If you want to end up back where you were, this will do it (although a waste of time imo).
cd first_folder/second_folder/ && zip -r name ./ && mv name.zip ${here} && cd -
(Thanks to @KarthikT for the "cd -" shortcut).